Theorem ofeq 7536

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 22	. 2 ⊢ (𝑅 = 𝑆 → 𝑅 = 𝑆)
2	1	ofeqd 7535	1 ⊢ (𝑅 = 𝑆 → ∘f 𝑅 = ∘f 𝑆)

Syntax hints:   → wi 4   = wceq 1539   ∘_f cof 7531

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 397  df-3an 1088  df-tru 1542  df-ex 1783  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-v 3434  df-in 3894  df-ss 3904  df-uni 4840  df-br 5075  df-opab 5137  df-mpt 5158  df-iota 6391  df-fv 6441  df-ov 7278  df-oprab 7279  df-mpo 7280  df-of 7533

This theorem is referenced by:  resspsrvsca  21187  sitmval  32316  mhphf2  40286  mendplusgfval  41010  mendvscafval  41015