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Theorem fvco3d 38282
Description: Natural deduction form of fvco3 6262. (Contributed by Stanislas Polu, 9-Mar-2020.)
Hypotheses
Ref Expression
fvco3d.1 (𝜑𝐺:𝐴𝐵)
fvco3d.2 (𝜑𝐶𝐴)
Assertion
Ref Expression
fvco3d (𝜑 → ((𝐹𝐺)‘𝐶) = (𝐹‘(𝐺𝐶)))

Proof of Theorem fvco3d
StepHypRef Expression
1 fvco3d.1 . 2 (𝜑𝐺:𝐴𝐵)
2 fvco3d.2 . 2 (𝜑𝐶𝐴)
3 fvco3 6262 . 2 ((𝐺:𝐴𝐵𝐶𝐴) → ((𝐹𝐺)‘𝐶) = (𝐹‘(𝐺𝐶)))
41, 2, 3syl2anc 692 1 (𝜑 → ((𝐹𝐺)‘𝐶) = (𝐹‘(𝐺𝐶)))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1481  wcel 1988  ccom 5108  wf 5872  cfv 5876
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1720  ax-4 1735  ax-5 1837  ax-6 1886  ax-7 1933  ax-8 1990  ax-9 1997  ax-10 2017  ax-11 2032  ax-12 2045  ax-13 2244  ax-ext 2600  ax-sep 4772  ax-nul 4780  ax-pow 4834  ax-pr 4897
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3an 1038  df-tru 1484  df-ex 1703  df-nf 1708  df-sb 1879  df-eu 2472  df-mo 2473  df-clab 2607  df-cleq 2613  df-clel 2616  df-nfc 2751  df-ne 2792  df-ral 2914  df-rex 2915  df-rab 2918  df-v 3197  df-sbc 3430  df-dif 3570  df-un 3572  df-in 3574  df-ss 3581  df-nul 3908  df-if 4078  df-sn 4169  df-pr 4171  df-op 4175  df-uni 4428  df-br 4645  df-opab 4704  df-id 5014  df-xp 5110  df-rel 5111  df-cnv 5112  df-co 5113  df-dm 5114  df-rn 5115  df-res 5116  df-ima 5117  df-iota 5839  df-fun 5878  df-fn 5879  df-f 5880  df-fv 5884
This theorem is referenced by:  extoimad  38284  imo72b2lem0  38285  imo72b2lem1  38291
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