Theorem ndsubaddl-P7.24b 852

Description: Natural Deduction: Function Substitution Rule ('+' left).

Hypothesis

Ref	Expression
ndsubaddl-P7.24b.1	⊢ (𝛾 → 𝑡 = 𝑢)

Assertion

Ref	Expression
ndsubaddl-P7.24b	⊢ (𝛾 → (𝑡 + 𝑤) = (𝑢 + 𝑤))

Proof of Theorem ndsubaddl-P7.24b

Step	Hyp	Ref	Expression
1		ndsubaddl-P7.24b.1	. 2 ⊢ (𝛾 → 𝑡 = 𝑢)
2	1	subaddl-P5 645	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:  ndsubaddd-P7  858  ndsubaddl-P7.24b.RC  898  ndsubaddl-P7.24b.CL  918