Theorem ofeq 7630

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 7629	1 ⊢ (𝑅 = 𝑆 → ∘f 𝑅 = ∘f 𝑆)

Syntax hints:   → wi 4   = wceq 1547   ∘_f cof 7625

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-ext 2712

This theorem depends on definitions:  df-bi 208  df-an 397  df-3an 1094  df-tru 1550  df-ex 1787  df-sb 2074  df-clab 2719  df-cleq 2732  df-clel 2815  df-v 3434  df-ss 3907  df-uni 4846  df-br 5080  df-opab 5142  df-mpt 5161  df-iota 6448  df-fv 6500  df-ov 7366  df-oprab 7367  df-mpo 7368  df-of 7627

This theorem is referenced by:  resspsrvsca  21958  sitmval  34540  mhphf2  43049  mendplusgfval  43627  mendvscafval  43632