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Theorem feq1dd 42703
Description: Equality deduction for functions. (Contributed by Glauco Siliprandi, 11-Dec-2019.)
Hypotheses
Ref Expression
feq1dd.eq (𝜑𝐹 = 𝐺)
feq1dd.f (𝜑𝐹:𝐴𝐵)
Assertion
Ref Expression
feq1dd (𝜑𝐺:𝐴𝐵)

Proof of Theorem feq1dd
StepHypRef Expression
1 feq1dd.f . 2 (𝜑𝐹:𝐴𝐵)
2 feq1dd.eq . . 3 (𝜑𝐹 = 𝐺)
32feq1d 6585 . 2 (𝜑 → (𝐹:𝐴𝐵𝐺:𝐴𝐵))
41, 3mpbid 231 1 (𝜑𝐺:𝐴𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1539  wf 6429
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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2709
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-3an 1088  df-tru 1542  df-fal 1552  df-ex 1783  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-rab 3073  df-v 3434  df-dif 3890  df-un 3892  df-in 3894  df-ss 3904  df-nul 4257  df-if 4460  df-sn 4562  df-pr 4564  df-op 4568  df-br 5075  df-opab 5137  df-rel 5596  df-cnv 5597  df-co 5598  df-dm 5599  df-rn 5600  df-fun 6435  df-fn 6436  df-f 6437
This theorem is referenced by:  cncficcgt0  43429  itgsubsticclem  43516  itgsbtaddcnst  43523  fourierdlem103  43750  fourierdlem104  43751  fourierdlem113  43760  ismeannd  44005  hoidmv1le  44132
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