Theorem ofeq 7696

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 7695	1 ⊢ (𝑅 = 𝑆 → ∘f 𝑅 = ∘f 𝑆)

This proof depends on syntax axioms:   → wi 4   = wceq 1569   ∘_f cof 7691

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-8 2146  ax-9 2154  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-3an 1105  df-tru 1572  df-ex 1812  df-sb 2099  df-clab 2739  df-cleq 2752  df-clel 2835  df-v 3452  df-ss 3896  df-uni 4867  df-br 5103  df-opab 5167  df-mpt 5186  df-iota 6494  df-fv 6546  df-ov 7423  df-oprab 7424  df-mpo 7425  df-of 7693

This theorem is used by:  resspsrvsca  22289  sitmval  35027  mhphf2  43719  mendplusgfval  44276  mendvscafval  44281