Theorem ofeq 7659

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 7658	1 ⊢ (𝑅 = 𝑆 → ∘f 𝑅 = ∘f 𝑆)

Syntax hints:   → wi 4   = wceq 1540   ∘_f cof 7654

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2702

This theorem depends on definitions:  df-bi 207  df-an 396  df-3an 1088  df-tru 1543  df-ex 1780  df-sb 2066  df-clab 2709  df-cleq 2722  df-clel 2804  df-v 3452  df-ss 3934  df-uni 4875  df-br 5111  df-opab 5173  df-mpt 5192  df-iota 6467  df-fv 6522  df-ov 7393  df-oprab 7394  df-mpo 7395  df-of 7656

This theorem is referenced by:  resspsrvsca  21893  sitmval  34347  mhphf2  42593  mendplusgfval  43177  mendvscafval  43182