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Theorem ffdmd 6749
Description: The domain of a function. (Contributed by Glauco Siliprandi, 26-Jun-2021.)
Hypothesis
Ref Expression
ffdmd.1 (𝜑𝐹:𝐴𝐵)
Assertion
Ref Expression
ffdmd (𝜑𝐹:dom 𝐹𝐵)

Proof of Theorem ffdmd
StepHypRef Expression
1 ffdmd.1 . . 3 (𝜑𝐹:𝐴𝐵)
2 ffdm 6748 . . 3 (𝐹:𝐴𝐵 → (𝐹:dom 𝐹𝐵 ∧ dom 𝐹𝐴))
31, 2syl 17 . 2 (𝜑 → (𝐹:dom 𝐹𝐵 ∧ dom 𝐹𝐴))
43simpld 496 1 (𝜑𝐹:dom 𝐹𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 397  wss 3949  dom cdm 5677  wf 6540
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-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3477  df-in 3956  df-ss 3966  df-fn 6547  df-f 6548
This theorem is referenced by:  ordtypelem5  9517  ablfaclem2  19956  ablfac2  19959  f1lindf  21377  lmcnp  22808  upgr1e  28373  upgrres1  28570  umgrres1  28571  umgr2v2e  28782  pliguhgr  29739  s3f1  32113  ccatf1  32115  swrdf1  32120  tocyccntz  32303  dfac21  41808  xlimmnfvlem1  44548  xlimpnfvlem1  44552  itgperiod  44697  issmfd  45451  issmfdf  45453  cnfsmf  45456  issmfled  45473  issmfgtd  45477  smfsuplem1  45527
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