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Theorem fcod 40864
Description: Composition of two mappings. (Contributed by Glauco Siliprandi, 26-Jun-2021.)
Hypotheses
Ref Expression
fcod.1 (𝜑𝐹:𝐵𝐶)
fcod.2 (𝜑𝐺:𝐴𝐵)
Assertion
Ref Expression
fcod (𝜑 → (𝐹𝐺):𝐴𝐶)

Proof of Theorem fcod
StepHypRef Expression
1 fcod.1 . 2 (𝜑𝐹:𝐵𝐶)
2 fcod.2 . 2 (𝜑𝐺:𝐴𝐵)
3 fco 6355 . 2 ((𝐹:𝐵𝐶𝐺:𝐴𝐵) → (𝐹𝐺):𝐴𝐶)
41, 2, 3syl2anc 576 1 (𝜑 → (𝐹𝐺):𝐴𝐶)
Colors of variables: wff setvar class
Syntax hints:  wi 4  ccom 5404  wf 6178
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1758  ax-4 1772  ax-5 1869  ax-6 1928  ax-7 1964  ax-8 2050  ax-9 2057  ax-10 2077  ax-11 2091  ax-12 2104  ax-13 2299  ax-ext 2745  ax-sep 5054  ax-nul 5061  ax-pr 5180
This theorem depends on definitions:  df-bi 199  df-an 388  df-or 834  df-3an 1070  df-tru 1510  df-ex 1743  df-nf 1747  df-sb 2014  df-mo 2544  df-eu 2580  df-clab 2754  df-cleq 2765  df-clel 2840  df-nfc 2912  df-ral 3087  df-rex 3088  df-rab 3091  df-v 3411  df-dif 3828  df-un 3830  df-in 3832  df-ss 3839  df-nul 4174  df-if 4345  df-sn 4436  df-pr 4438  df-op 4442  df-br 4924  df-opab 4986  df-id 5305  df-xp 5406  df-rel 5407  df-cnv 5408  df-co 5409  df-dm 5410  df-rn 5411  df-fun 6184  df-fn 6185  df-f 6186
This theorem is referenced by: (None)
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