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Theorem feq1dd 44570
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 6712 . 2 (𝜑 → (𝐹:𝐴𝐵𝐺:𝐴𝐵))
41, 3mpbid 231 1 (𝜑𝐺:𝐴𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1533  wf 6549
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 2699
This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2706  df-cleq 2720  df-clel 2806  df-rab 3431  df-v 3475  df-dif 3952  df-un 3954  df-in 3956  df-ss 3966  df-nul 4327  df-if 4533  df-sn 4633  df-pr 4635  df-op 4639  df-br 5153  df-opab 5215  df-rel 5689  df-cnv 5690  df-co 5691  df-dm 5692  df-rn 5693  df-fun 6555  df-fn 6556  df-f 6557
This theorem is referenced by:  cncficcgt0  45305  itgsubsticclem  45392  itgsbtaddcnst  45399  fourierdlem103  45626  fourierdlem104  45627  fourierdlem113  45636  ismeannd  45884  hoidmv1le  46011
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