Theorem subaddl-P5 645

Description: Left Substitution Law for '+'.

Hypothesis

Ref	Expression
subaddl-P5.1	⊢ (𝛾 → 𝑡 = 𝑢)

Assertion

Ref	Expression
subaddl-P5	⊢ (𝛾 → (𝑡 + 𝑤) = (𝑢 + 𝑤))

Proof of Theorem subaddl-P5

Step	Hyp	Ref	Expression
1		subaddl-P5.1	. 2 ⊢ (𝛾 → 𝑡 = 𝑢)
2		ax-L9-addl 23	. 2 ⊢ (𝑡 = 𝑢 → (𝑡 + 𝑤) = (𝑢 + 𝑤))
3	1, 2	syl-P3.24.RC 260	1 ⊢ (𝛾 → (𝑡 + 𝑤) = (𝑢 + 𝑤))

Syntax hints:   + term-add 4   = wff-equals 6   → wff-imp 10

This theorem was proved from axioms:  ax-L1 11  ax-L2 12  ax-L3 13  ax-MP 14  ax-L9-addl 23

This theorem depends on definitions:  df-bi-D2.1 107  df-and-D2.2 133  df-true-D2.4 155

This theorem is referenced by:  subaddd-P5  647  example-E5.02a  664  ndsubaddl-P7.24b  852