Transitive Property of Equality Variation 2
Sides of an Equilateral Triangle
Sides of an Equilateral Triangle 2
Distance Property 1
Angle Symmetry Example 2
Collinear Angles Property 9
Transitive Property Application 2
Angles of an Isosceles Triangle
Angles of an Isosceles Triangle 5
Angles of an Equilateral Triangle
Distance Property 2
Transitive Property of Equality Variation 3
Angle Symmetry Property 5
Angles of an Isosceles Triangle 4
Angles of an Isosceles Triangle 4 A
Angles of an Equilateral Triangle 2
Angles of an Equilateral Triangle 3
Transitive Property of Equality Variation 1
Propagated Transitive Property 3
Angles of an Equilateral Triangle 4
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
Substitute 2
Add Term to Both Sides 2
Multiplicative Identity 2
Distributive Property 4
Multiplicative Property of Equality Variation 1
Addition Theorem
Add Three
Divide Both Sides
Multiplicative Property of Equality Variation 2
Division is Commutative
Associative Property
Divide Each Side
Equilateral Triangle 60
Angles of an Equilateral Triangle 5
Angles of an Equilateral Triangle 6
Equilateral Triangle 60 2

Proof: Substitute 2

Let's prove the following theorem:

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

then a + d = c

Proof:

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

Given
1 a + b = c
2 d = b
Proof Table
# Claim Reason
1 b = d if d = b, then b = d
2 a + d = c if a + b = c and b = d, then a + d = c
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