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Theorem swopolem 4515
 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 2801 . 2
3 breq1 4218 . . . 4
4 breq1 4218 . . . . 5
54orbi1d 685 . . . 4
63, 5imbi12d 313 . . 3
7 breq2 4219 . . . 4
8 breq2 4219 . . . . 5
98orbi2d 684 . . . 4
107, 9imbi12d 313 . . 3
11 breq2 4219 . . . . 5
12 breq1 4218 . . . . 5
1311, 12orbi12d 692 . . . 4
1413imbi2d 309 . . 3
156, 10, 14rspc3v 3063 . 2
162, 15mpan9 457 1
 Colors of variables: wff set class Syntax hints:   wi 4   wo 359   wa 360   w3a 937   wceq 1653   wcel 1726  wral 2707   class class class wbr 4215 This theorem is referenced by:  swoer  6936  swoord1  6937  swoord2  6938 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-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-br 4216
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