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Theorem feq1dd 44420
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 6695 . 2 (𝜑 → (𝐹:𝐴𝐵𝐺:𝐴𝐵))
41, 3mpbid 231 1 (𝜑𝐺:𝐴𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1533  wf 6532
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-ext 2697
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-sb 2060  df-clab 2704  df-cleq 2718  df-clel 2804  df-rab 3427  df-v 3470  df-dif 3946  df-un 3948  df-in 3950  df-ss 3960  df-nul 4318  df-if 4524  df-sn 4624  df-pr 4626  df-op 4630  df-br 5142  df-opab 5204  df-rel 5676  df-cnv 5677  df-co 5678  df-dm 5679  df-rn 5680  df-fun 6538  df-fn 6539  df-f 6540
This theorem is referenced by:  cncficcgt0  45158  itgsubsticclem  45245  itgsbtaddcnst  45252  fourierdlem103  45479  fourierdlem104  45480  fourierdlem113  45489  ismeannd  45737  hoidmv1le  45864
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