Theorem subsucc-P5 644

Description: Substitution Law for 's‘'.

Hypothesis

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

Assertion

Ref	Expression
subsucc-P5	⊢ (𝛾 → s‘𝑡 = s‘𝑢)

Proof of Theorem subsucc-P5

Step	Hyp	Ref	Expression
1		subsucc-P5.1	. 2 ⊢ (𝛾 → 𝑡 = 𝑢)
2		ax-L9-succ 22	. 2 ⊢ (𝑡 = 𝑢 → s‘𝑡 = s‘𝑢)
3	1, 2	syl-P3.24.RC 260	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:  psubsuccv-P6-L1  805  ndsubsucc-P7.24a  851  ndsubsucc-P7.24a.RC  897