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Theorem stoweidlem6 27733
 Description: Lemma for stoweid 27790: 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 960 . 2
2 eleq1 2498 . . . . 5
323anbi3d 1261 . . . 4
4 stoweidlem6.2 . . . . . 6
5 fveq1 5729 . . . . . . . 8
65oveq2d 6099 . . . . . . 7
76adantr 453 . . . . . 6
84, 7mpteq2da 4296 . . . . 5
98eleq1d 2504 . . . 4
103, 9imbi12d 313 . . 3
11 simp2 959 . . . 4
12 eleq1 2498 . . . . . . 7
13123anbi2d 1260 . . . . . 6
14 stoweidlem6.1 . . . . . . . 8
15 fveq1 5729 . . . . . . . . . 10
1615oveq1d 6098 . . . . . . . . 9
1716adantr 453 . . . . . . . 8
1814, 17mpteq2da 4296 . . . . . . 7
1918eleq1d 2504 . . . . . 6
2013, 19imbi12d 313 . . . . 5
21 stoweidlem6.3 . . . . 5
2220, 21vtoclg 3013 . . . 4
2311, 22mpcom 35 . . 3
2410, 23vtoclg 3013 . 2
251, 24mpcom 35 1
 Colors of variables: wff set class Syntax hints:   wi 4   w3a 937  wnf 1554   wceq 1653   wcel 1726   cmpt 4268  cfv 5456  (class class class)co 6083   cmul 8997 This theorem is referenced by:  stoweidlem19  27746  stoweidlem22  27749  stoweidlem32  27759  stoweidlem36  27763 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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-3an 939  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-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4215  df-opab 4269  df-mpt 4270  df-iota 5420  df-fv 5464  df-ov 6086
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