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Theorem ofeq 7625
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
StepHypRef Expression
1 id 22 . 2 (𝑅 = 𝑆𝑅 = 𝑆)
21ofeqd 7624 1 (𝑅 = 𝑆 → ∘f 𝑅 = ∘f 𝑆)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1542  f cof 7620
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2708
This theorem depends on definitions:  df-bi 206  df-an 398  df-3an 1090  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2715  df-cleq 2729  df-clel 2815  df-v 3450  df-in 3922  df-ss 3932  df-uni 4871  df-br 5111  df-opab 5173  df-mpt 5194  df-iota 6453  df-fv 6509  df-ov 7365  df-oprab 7366  df-mpo 7367  df-of 7622
This theorem is referenced by:  resspsrvsca  21403  sitmval  32989  mhphf2  40801  mendplusgfval  41541  mendvscafval  41546
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