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Theorem swopolem 4795
 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:   ,,,   ,,,   ,,,   ,,,   ,,   ,
Allowed substitution hints:   ()   (,)

Proof of Theorem swopolem
StepHypRef Expression
1 swopolem.1 . . 3
21ralrimivvva 2863 . 2
3 breq1 4436 . . . 4
4 breq1 4436 . . . . 5
54orbi1d 702 . . . 4
63, 5imbi12d 320 . . 3
7 breq2 4437 . . . 4
8 breq2 4437 . . . . 5
98orbi2d 701 . . . 4
107, 9imbi12d 320 . . 3
11 breq2 4437 . . . . 5
12 breq1 4436 . . . . 5
1311, 12orbi12d 709 . . . 4
1413imbi2d 316 . . 3
156, 10, 14rspc3v 3206 . 2
162, 15mpan9 469 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wo 368   wa 369   w3a 972   wceq 1381   wcel 1802  wral 2791   class class class wbr 4433 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1603  ax-4 1616  ax-5 1689  ax-6 1732  ax-7 1774  ax-10 1821  ax-11 1826  ax-12 1838  ax-13 1983  ax-ext 2419 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 974  df-tru 1384  df-ex 1598  df-nf 1602  df-sb 1725  df-clab 2427  df-cleq 2433  df-clel 2436  df-nfc 2591  df-ral 2796  df-rab 2800  df-v 3095  df-dif 3461  df-un 3463  df-in 3465  df-ss 3472  df-nul 3768  df-if 3923  df-sn 4011  df-pr 4013  df-op 4017  df-br 4434 This theorem is referenced by:  swoer  7337  swoord1  7338  swoord2  7339
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