Theorem ofeq 7690

Description: Equality theorem for function operation. (Contributed by Mario Carneiro, 20-Jul-2014.)

Assertion

Ref	Expression
ofeq	⊢ (𝑅 = 𝑆 → ∘f 𝑅 = ∘f 𝑆)

Proof of Theorem ofeq

Step	Hyp	Ref	Expression
1		id 23	. 2 ⊢ (𝑅 = 𝑆 → 𝑅 = 𝑆)
2	1	ofeqd 7689	1 ⊢ (𝑅 = 𝑆 → ∘f 𝑅 = ∘f 𝑆)

This proof depends on syntax axioms:   → wi 4   = wceq 1570   ∘_f cof 7685

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2148  ax-9 2156  ax-ext 2738

This proof depends on definitions:  df-bi 210  df-an 402  df-3an 1105  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2745  df-cleq 2758  df-clel 2841  df-v 3460  df-ss 3925  df-uni 4878  df-br 5115  df-opab 5179  df-mpt 5198  df-iota 6499  df-fv 6551  df-ov 7426  df-oprab 7427  df-mpo 7428  df-of 7687

This theorem is used by:  resspsrvsca  22156  sitmval  34763  mhphf2  43363  mendplusgfval  43941  mendvscafval  43946