Multiplicative Identity 2

Commutative Property Variation 1

Substitution 2

Distributive Property 4

Multiplicative Property of Equality Variation 1

Addition Theorem

Transitive Property of Equality Variation 2

Double

Transitive Property of Equality Variation 1

Divide Both Sides

Multiplicative Property of Equality Variation 2

Transitive Property of Equality Variation 3

Division is Commutative

Associative Property

Divide Each Side

Reduce Addition 2

Proof: Reduce Addition 2

Let's prove the following theorem:

if a + a = 90, then a = 45

Proof:

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Given

1	a + a = 90

Proof Table

#	Claim	Reason
1	a ⋅ 2 = 90	if a + a = 90, then a ⋅ 2 = 90 (double)
2	a = 90 / 2	if a ⋅ 2 = 90, then a = 90 / 2 (Divide Each Side)
3	90 / 2 = 45	90 / 2 = 45 (Fixed Value Statement)
4	a = 45	if a = 90 / 2 and 90 / 2 = 45, then a = 45 (Transitive Property of Equality)

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