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Theorem fco2d 43515
Description: Natural deduction form of fco2 6744. (Contributed by Stanislas Polu, 9-Mar-2020.)
Hypotheses
Ref Expression
fco2d.1 (𝜑𝐺:𝐴𝐵)
fco2d.2 (𝜑 → (𝐹𝐵):𝐵𝐶)
Assertion
Ref Expression
fco2d (𝜑 → (𝐹𝐺):𝐴𝐶)

Proof of Theorem fco2d
StepHypRef Expression
1 fco2d.2 . 2 (𝜑 → (𝐹𝐵):𝐵𝐶)
2 fco2d.1 . 2 (𝜑𝐺:𝐴𝐵)
3 fco2 6744 . 2 (((𝐹𝐵):𝐵𝐶𝐺:𝐴𝐵) → (𝐹𝐺):𝐴𝐶)
41, 2, 3syl2anc 583 1 (𝜑 → (𝐹𝐺):𝐴𝐶)
Colors of variables: wff setvar class
Syntax hints:  wi 4  cres 5674  ccom 5676  wf 6538
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-10 2130  ax-11 2147  ax-12 2164  ax-ext 2698  ax-sep 5293  ax-nul 5300  ax-pr 5423
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 847  df-3an 1087  df-tru 1537  df-fal 1547  df-ex 1775  df-nf 1779  df-sb 2061  df-mo 2529  df-eu 2558  df-clab 2705  df-cleq 2719  df-clel 2805  df-nfc 2880  df-ral 3057  df-rex 3066  df-rab 3428  df-v 3471  df-dif 3947  df-un 3949  df-in 3951  df-ss 3961  df-nul 4319  df-if 4525  df-sn 4625  df-pr 4627  df-op 4631  df-br 5143  df-opab 5205  df-id 5570  df-xp 5678  df-rel 5679  df-cnv 5680  df-co 5681  df-dm 5682  df-rn 5683  df-res 5684  df-ima 5685  df-fun 6544  df-fn 6545  df-f 6546
This theorem is referenced by:  extoimad  43517  imo72b2lem0  43518  imo72b2lem2  43520  imo72b2lem1  43522  imo72b2  43525
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