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Theorem stoweidlem4 27743
 Description: Lemma for stoweid 27802: a class variable replaces a set variable, for constant functions. (Contributed by Glauco Siliprandi, 20-Apr-2017.)
Hypothesis
Ref Expression
stoweidlem4.1
Assertion
Ref Expression
stoweidlem4
Distinct variable groups:   ,,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem stoweidlem4
StepHypRef Expression
1 eleq1 2498 . . . . 5
21anbi2d 686 . . . 4
3 simpl 445 . . . . . 6
43mpteq2dva 4298 . . . . 5
54eleq1d 2504 . . . 4
62, 5imbi12d 313 . . 3
7 stoweidlem4.1 . . 3
86, 7vtoclg 3013 . 2
98anabsi7 794 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   wceq 1653   wcel 1726   cmpt 4269  cr 8994 This theorem is referenced by:  stoweidlem18  27757  stoweidlem19  27758  stoweidlem22  27761  stoweidlem32  27771  stoweidlem36  27775  stoweidlem40  27779  stoweidlem41  27780  stoweidlem55  27794 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-v 2960  df-opab 4270  df-mpt 4271
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