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

Proof: Double

Let's prove the following theorem:

if a + a = b, then a ⋅ 2 = b

Proof:

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Given

1	a + a = b

Proof Table

#	Claim	Reason
1	a + a = a ⋅ 2	a + a = a ⋅ 2 (addition_theorem)
2	a ⋅ 2 = b	if a + a = a ⋅ 2 and a + a = b, then a ⋅ 2 = b (Transitive Property of Equality Variation 2)

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