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Theorem fco2d 43403
Description: Natural deduction form of fco2 6734. (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 6734 . 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 5668  ccom 5670  wf 6529
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-10 2129  ax-11 2146  ax-12 2163  ax-ext 2695  ax-sep 5289  ax-nul 5296  ax-pr 5417
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-nf 1778  df-sb 2060  df-mo 2526  df-eu 2555  df-clab 2702  df-cleq 2716  df-clel 2802  df-nfc 2877  df-ral 3054  df-rex 3063  df-rab 3425  df-v 3468  df-dif 3943  df-un 3945  df-in 3947  df-ss 3957  df-nul 4315  df-if 4521  df-sn 4621  df-pr 4623  df-op 4627  df-br 5139  df-opab 5201  df-id 5564  df-xp 5672  df-rel 5673  df-cnv 5674  df-co 5675  df-dm 5676  df-rn 5677  df-res 5678  df-ima 5679  df-fun 6535  df-fn 6536  df-f 6537
This theorem is referenced by:  extoimad  43405  imo72b2lem0  43406  imo72b2lem2  43408  imo72b2lem1  43410  imo72b2  43413
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