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Theorem stoweidlem8 27747
 Description: Lemma for stoweid 27802: two class variables replace two set variables, for the sum of two functions. (Contributed by Glauco Siliprandi, 20-Apr-2017.)
Hypotheses
Ref Expression
stoweidlem8.1
stoweidlem8.2
stoweidlem8.3
Assertion
Ref Expression
stoweidlem8
Distinct variable groups:   ,,   ,,   ,,   ,,   ,,   ,
Allowed substitution hints:   ()   ()   ()   ()   (,)

Proof of Theorem stoweidlem8
StepHypRef Expression
1 simp3 960 . 2
2 eleq1 2498 . . . . 5
323anbi3d 1261 . . . 4
4 stoweidlem8.3 . . . . . . 7
54nfeq2 2585 . . . . . 6
6 fveq1 5730 . . . . . . . 8
76oveq2d 6100 . . . . . . 7
87adantr 453 . . . . . 6
95, 8mpteq2da 4297 . . . . 5
109eleq1d 2504 . . . 4
113, 10imbi12d 313 . . 3
12 simp2 959 . . . 4
13 eleq1 2498 . . . . . . 7
14133anbi2d 1260 . . . . . 6
15 stoweidlem8.2 . . . . . . . . 9
1615nfeq2 2585 . . . . . . . 8
17 fveq1 5730 . . . . . . . . . 10
1817oveq1d 6099 . . . . . . . . 9
1918adantr 453 . . . . . . . 8
2016, 19mpteq2da 4297 . . . . . . 7
2120eleq1d 2504 . . . . . 6
2214, 21imbi12d 313 . . . . 5
23 stoweidlem8.1 . . . . 5
2422, 23vtoclg 3013 . . . 4
2512, 24mpcom 35 . . 3
2611, 25vtoclg 3013 . 2
271, 26mpcom 35 1
 Colors of variables: wff set class Syntax hints:   wi 4   w3a 937   wceq 1653   wcel 1726  wnfc 2561   cmpt 4269  cfv 5457  (class class class)co 6084   caddc 8998 This theorem is referenced by:  stoweidlem20  27759  stoweidlem21  27760  stoweidlem22  27761  stoweidlem23  27762 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-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 4216  df-opab 4270  df-mpt 4271  df-iota 5421  df-fv 5465  df-ov 6087
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