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Theorem stoweidlem4 27856
 Description: Lemma for stoweid 27915: 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 simpr 447 . . 3
2 eleq1 2356 . . . . . 6
32anbi2d 684 . . . . 5
4 nfv 1609 . . . . . . 7
5 simpl 443 . . . . . . 7
64, 5mpteq2da 4121 . . . . . 6
76eleq1d 2362 . . . . 5
83, 7imbi12d 311 . . . 4
9 stoweidlem4.1 . . . . 5
10 ax-1 5 . . . . 5
119, 10ax-mp 8 . . . 4
128, 11vtoclga 2862 . . 3
131, 12syl 15 . 2
1413pm2.43i 43 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 358   wceq 1632   wcel 1696   cmpt 4093  cr 8752 This theorem is referenced by:  stoweidlem18  27870  stoweidlem19  27871  stoweidlem22  27874  stoweidlem32  27884  stoweidlem36  27888  stoweidlem40  27892  stoweidlem41  27893  stoweidlem55  27907 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ral 2561  df-v 2803  df-opab 4094  df-mpt 4095
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