Transitive Property of Equality Variation 2
Distance Property 1
Distance Property 2
Distance Property 3
Angle Symmetry Example 2
Collinear Angles Property 9
Transitive Property Application 2
Angles of an Isosceles Triangle
Angle Symmetry Example
Angle Symmetry 2
Isosceles Triangle 2
Transitive Property of Equality Variation 1
Perpendicular to Angle
Collinear Then 180
Subtract Both Sides
Add Term to Both Sides 6
Subtract Both Sides 2
Add Term to Both Sides 7
Vertical Angles
Angle Addition Theorem
Collinear Angles B
Exterior Angle
Exterior Angle B
Collinear Angles Property 10
Collinear Angles Property 3
Collinear Angles Property 3 B
Collinear Angles Property 3 C
alternate interior angles then parallel
ParallelThenAIA
Parallelthenaiashort
Commutative Property Example 2
Commutative Property Variation 1
Substitution 2
Substitution 8
Angle Symmetry B
Substitution Example 10
Substitute First Term
Triangles Sum to 180
Equality Example
If Two Angles Equal Then Three Angles Equal
Angle Angle Side Triangle
Altitudes Isosceles

Proof: Substitute First Term

Let's prove the following theorem:

if the following are true:
  • (a + b) + c = d
  • a = e

then (e + b) + c = d

Proof:

View as a tree | View dependent proofs | Try proving it

Given
1 (a + b) + c = d
2 a = e
Proof Table
# Claim Reason
1 (a + b) + c = a + (b + c) (a + b) + c = a + (b + c)
2 (b + c) + a = a + (b + c) (b + c) + a = a + (b + c)
3 a + (b + c) = (a + b) + c if (a + b) + c = a + (b + c), then a + (b + c) = (a + b) + c
4 (b + c) + a = (a + b) + c if (b + c) + a = a + (b + c) and a + (b + c) = (a + b) + c, then (b + c) + a = (a + b) + c
5 (b + c) + a = d if (b + c) + a = (a + b) + c and (a + b) + c = d, then (b + c) + a = d
6 (b + c) + e = d if (b + c) + a = d and a = e, then (b + c) + e = d
7 e + (b + c) = d if (b + c) + e = d, then e + (b + c) = d
8 (e + b) + c = e + (b + c) (e + b) + c = e + (b + c)
9 (e + b) + c = d if (e + b) + c = e + (b + c) and e + (b + c) = d, then (e + b) + c = d
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