Theorem ofeq 7667

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 7666	1 ⊢ (𝑅 = 𝑆 → ∘f 𝑅 = ∘f 𝑆)

Syntax hints:   → wi 4   = wceq 1563   ∘_f cof 7662

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1818  ax-4 1832  ax-5 1933  ax-6 1990  ax-7 2031  ax-8 2147  ax-9 2155  ax-ext 2737

This theorem depends on definitions:  df-bi 210  df-an 401  df-3an 1103  df-tru 1566  df-ex 1803  df-sb 2094  df-clab 2744  df-cleq 2757  df-clel 2840  df-v 3459  df-ss 3924  df-uni 4869  df-br 5106  df-opab 5168  df-mpt 5187  df-iota 6481  df-fv 6533  df-ov 7403  df-oprab 7404  df-mpo 7405  df-of 7664

This theorem is referenced by:  resspsrvsca  22086  sitmval  34656  mhphf2  43192  mendplusgfval  43770  mendvscafval  43775