Theorem ofeq 7723

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 7722	1 ⊢ (𝑅 = 𝑆 → ∘f 𝑅 = ∘f 𝑆)

This proof depends on syntax axioms:   → wi 4   = wceq 1570   ∘_f cof 7718

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 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-3an 1105  df-tru 1573  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-v 3456  df-ss 3901  df-uni 4871  df-br 5107  df-opab 5172  df-mpt 5191  df-iota 6515  df-fv 6569  df-ov 7449  df-oprab 7450  df-mpo 7451  df-of 7720

This theorem is used by:  resspsrvsca  22317  sitmval  35064  mhphf2  43830  mendplusgfval  44386  mendvscafval  44391