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Theorem swopolem 4814
Description: Perform the substitutions into the strict weak ordering law. (Contributed by Mario Carneiro, 31-Dec-2014.)
Hypothesis
Ref Expression
swopolem.1
Assertion
Ref Expression
swopolem
Distinct variable groups:   , , ,   , , ,   , , ,   , , ,   , ,   ,

Proof of Theorem swopolem
StepHypRef Expression
1 swopolem.1 . . 3
21ralrimivvva 2879 . 2
3 breq1 4455 . . . 4
4 breq1 4455 . . . . 5
54orbi1d 702 . . . 4
63, 5imbi12d 320 . . 3
7 breq2 4456 . . . 4
8 breq2 4456 . . . . 5
98orbi2d 701 . . . 4
107, 9imbi12d 320 . . 3
11 breq2 4456 . . . . 5
12 breq1 4455 . . . . 5
1311, 12orbi12d 709 . . . 4
1413imbi2d 316 . . 3
156, 10, 14rspc3v 3222 . 2
162, 15mpan9 469 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  \/wo 368  /\wa 369  /\w3a 973  =wceq 1395  e.wcel 1818  A.wral 2807   class class class wbr 4452
This theorem is referenced by:  swoer  7358  swoord1  7359  swoord2  7360
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453
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