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Theorem ofeq 7669
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 7668 1 (𝑅 = 𝑆 → ∘f 𝑅 = ∘f 𝑆)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1541  f cof 7664
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2703
This theorem depends on definitions:  df-bi 206  df-an 397  df-3an 1089  df-tru 1544  df-ex 1782  df-sb 2068  df-clab 2710  df-cleq 2724  df-clel 2810  df-v 3476  df-in 3954  df-ss 3964  df-uni 4908  df-br 5148  df-opab 5210  df-mpt 5231  df-iota 6492  df-fv 6548  df-ov 7408  df-oprab 7409  df-mpo 7410  df-of 7666
This theorem is referenced by:  resspsrvsca  21529  sitmval  33336  mhphf2  41167  mendplusgfval  41912  mendvscafval  41917
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