Theorem ndsubaddr-P7.24c 853

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

Hypothesis

Ref	Expression
ndsubaddr-P7.24c.1	⊢ (𝛾 → 𝑡 = 𝑢)

Assertion

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

Proof of Theorem ndsubaddr-P7.24c

Step	Hyp	Ref	Expression
1		ndsubaddr-P7.24c.1	. 2 ⊢ (𝛾 → 𝑡 = 𝑢)
2	1	subaddr-P5 646	1 ⊢ (𝛾 → (𝑤 + 𝑡) = (𝑤 + 𝑢))

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-addr 24

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  ndsubaddr-P7.24c.RC  899  ndsubaddr-P7.24c.CL  919