Theorem ndsubsucc-P7.24a 851

Description: Natural Deduction: Function Substitution Rule ('s‘').

Hypothesis

Ref	Expression
ndsubsucc-P7.24a.1	⊢ (𝛾 → 𝑡 = 𝑢)

Assertion

Ref	Expression
ndsubsucc-P7.24a	⊢ (𝛾 → s‘𝑡 = s‘𝑢)

Proof of Theorem ndsubsucc-P7.24a

Step	Hyp	Ref	Expression
1		ndsubsucc-P7.24a.1	. 2 ⊢ (𝛾 → 𝑡 = 𝑢)
2	1	subsucc-P5 644	1 ⊢ (𝛾 → s‘𝑡 = s‘𝑢)

Syntax hints:  s‘term_succ 3   = 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-succ 22

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:  ndsubsucc-P7.24a.CL  917