Theorem ofeq 7677

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 7676	1 ⊢ (𝑅 = 𝑆 → ∘f 𝑅 = ∘f 𝑆)

Syntax hints:   → wi 4   = wceq 1568   ∘_f cof 7672

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1823  ax-4 1837  ax-5 1938  ax-6 1995  ax-7 2036  ax-8 2143  ax-9 2151  ax-ext 2733

This theorem depends on definitions:  df-bi 210  df-an 401  df-3an 1103  df-tru 1571  df-ex 1808  df-sb 2095  df-clab 2740  df-cleq 2753  df-clel 2836  df-v 3455  df-ss 3921  df-uni 4872  df-br 5109  df-opab 5173  df-mpt 5192  df-iota 6492  df-fv 6544  df-ov 7413  df-oprab 7414  df-mpo 7415  df-of 7674

This theorem is referenced by:  resspsrvsca  22105  sitmval  34705  mhphf2  43300  mendplusgfval  43878  mendvscafval  43883