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Theorem feq1dd 39846
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 6191 . 2 (𝜑 → (𝐹:𝐴𝐵𝐺:𝐴𝐵))
41, 3mpbid 222 1 (𝜑𝐺:𝐴𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1632  wf 6045
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-9 2148  ax-10 2168  ax-11 2183  ax-12 2196  ax-13 2391  ax-ext 2740
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-3an 1074  df-tru 1635  df-ex 1854  df-nf 1859  df-sb 2047  df-clab 2747  df-cleq 2753  df-clel 2756  df-nfc 2891  df-rab 3059  df-v 3342  df-dif 3718  df-un 3720  df-in 3722  df-ss 3729  df-nul 4059  df-if 4231  df-sn 4322  df-pr 4324  df-op 4328  df-br 4805  df-opab 4865  df-rel 5273  df-cnv 5274  df-co 5275  df-dm 5276  df-rn 5277  df-fun 6051  df-fn 6052  df-f 6053
This theorem is referenced by:  cncficcgt0  40604  itgsubsticclem  40694  itgsbtaddcnst  40701  fourierdlem103  40929  fourierdlem104  40930  fourierdlem113  40939  ismeannd  41187  hoidmv1le  41314
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