Theorem ofeq 7685

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 7684	1 ⊢ (𝑅 = 𝑆 → ∘f 𝑅 = ∘f 𝑆)

This proof depends on syntax axioms:   → wi 4   = wceq 1570   ∘_f cof 7680

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 2147  ax-9 2155  ax-ext 2733

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 2740  df-cleq 2753  df-clel 2836  df-v 3453  df-ss 3916  df-uni 4868  df-br 5104  df-opab 5168  df-mpt 5187  df-iota 6487  df-fv 6539  df-ov 7415  df-oprab 7416  df-mpo 7417  df-of 7682

This theorem is used by:  resspsrvsca  22261  sitmval  34961  mhphf2  43585  mendplusgfval  44138  mendvscafval  44143