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Theorem fco2d 42847
Description: Natural deduction form of fco2 6741. (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 6741 . 2 (((𝐹𝐵):𝐵𝐶𝐺:𝐴𝐵) → (𝐹𝐺):𝐴𝐶)
41, 2, 3syl2anc 585 1 (𝜑 → (𝐹𝐺):𝐴𝐶)
Colors of variables: wff setvar class
Syntax hints:  wi 4  cres 5677  ccom 5679  wf 6536
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-10 2138  ax-11 2155  ax-12 2172  ax-ext 2704  ax-sep 5298  ax-nul 5305  ax-pr 5426
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1783  df-nf 1787  df-sb 2069  df-mo 2535  df-eu 2564  df-clab 2711  df-cleq 2725  df-clel 2811  df-nfc 2886  df-ral 3063  df-rex 3072  df-rab 3434  df-v 3477  df-dif 3950  df-un 3952  df-in 3954  df-ss 3964  df-nul 4322  df-if 4528  df-sn 4628  df-pr 4630  df-op 4634  df-br 5148  df-opab 5210  df-id 5573  df-xp 5681  df-rel 5682  df-cnv 5683  df-co 5684  df-dm 5685  df-rn 5686  df-res 5687  df-ima 5688  df-fun 6542  df-fn 6543  df-f 6544
This theorem is referenced by:  extoimad  42849  imo72b2lem0  42850  imo72b2lem2  42852  imo72b2lem1  42854  imo72b2  42857
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