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Theorem stoweidlem6 27755
 Description: Lemma for stoweid 27812: two class variables replace two set variables, for multiplication of two functions. (Contributed by Glauco Siliprandi, 20-Apr-2017.)
Hypotheses
Ref Expression
stoweidlem6.1
stoweidlem6.2
stoweidlem6.3
Assertion
Ref Expression
stoweidlem6
Distinct variable groups:   ,,   ,,   ,,   ,,   ,,   ,
Allowed substitution hints:   ()   ()   ()   ()   (,)

Proof of Theorem stoweidlem6
StepHypRef Expression
1 simp3 957 . . 3
2 eleq1 2343 . . . . . 6
323anbi3d 1258 . . . . 5
4 stoweidlem6.2 . . . . . . 7
5 fveq1 5524 . . . . . . . . 9
65oveq2d 5874 . . . . . . . 8
76adantr 451 . . . . . . 7
84, 7mpteq2da 4105 . . . . . 6
98eleq1d 2349 . . . . 5
103, 9imbi12d 311 . . . 4
11 simp2 956 . . . . . . 7
12 eleq1 2343 . . . . . . . . . 10
13123anbi2d 1257 . . . . . . . . 9
14 stoweidlem6.1 . . . . . . . . . . 11
15 fveq1 5524 . . . . . . . . . . . . 13
1615oveq1d 5873 . . . . . . . . . . . 12
1716adantr 451 . . . . . . . . . . 11
1814, 17mpteq2da 4105 . . . . . . . . . 10
1918eleq1d 2349 . . . . . . . . 9
2013, 19imbi12d 311 . . . . . . . 8
21 stoweidlem6.3 . . . . . . . . 9
2221a1i 10 . . . . . . . 8
2320, 22vtoclga 2849 . . . . . . 7
2411, 23syl 15 . . . . . 6
2524pm2.43i 43 . . . . 5
2625a1i 10 . . . 4
2710, 26vtoclga 2849 . . 3
281, 27syl 15 . 2
2928pm2.43i 43 1
 Colors of variables: wff set class Syntax hints:   wi 4   w3a 934  wnf 1531   wceq 1623   wcel 1684   cmpt 4077  cfv 5255  (class class class)co 5858   cmul 8742 This theorem is referenced by:  stoweidlem19  27768  stoweidlem22  27771  stoweidlem32  27781  stoweidlem36  27785 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-uni 3828  df-br 4024  df-opab 4078  df-mpt 4079  df-iota 5219  df-fv 5263  df-ov 5861
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