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Theorem feq1dd 42225
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 6483 . 2 (𝜑 → (𝐹:𝐴𝐵𝐺:𝐴𝐵))
41, 3mpbid 235 1 (𝜑𝐺:𝐴𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1542  wf 6329
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1916  ax-6 1974  ax-7 2019  ax-8 2115  ax-9 2123  ax-ext 2710
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 847  df-3an 1090  df-tru 1545  df-ex 1787  df-sb 2074  df-clab 2717  df-cleq 2730  df-clel 2811  df-v 3399  df-un 3846  df-in 3848  df-ss 3858  df-sn 4514  df-pr 4516  df-op 4520  df-br 5028  df-opab 5090  df-rel 5526  df-cnv 5527  df-co 5528  df-dm 5529  df-rn 5530  df-fun 6335  df-fn 6336  df-f 6337
This theorem is referenced by:  cncficcgt0  42955  itgsubsticclem  43042  itgsbtaddcnst  43049  fourierdlem103  43276  fourierdlem104  43277  fourierdlem113  43286  ismeannd  43531  hoidmv1le  43658
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