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Theorem swopolem 4227
 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 2515 . 2
3 breq1 3932 . . . 4
4 breq1 3932 . . . . 5
54orbi1d 780 . . . 4
63, 5imbi12d 233 . . 3
7 breq2 3933 . . . 4
8 breq2 3933 . . . . 5
98orbi2d 779 . . . 4
107, 9imbi12d 233 . . 3
11 breq2 3933 . . . . 5
12 breq1 3932 . . . . 5
1311, 12orbi12d 782 . . . 4
1413imbi2d 229 . . 3
156, 10, 14rspc3v 2805 . 2
162, 15mpan9 279 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wo 697   w3a 962   wceq 1331   wcel 1480  wral 2416   class class class wbr 3929 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421  df-v 2688  df-un 3075  df-sn 3533  df-pr 3534  df-op 3536  df-br 3930 This theorem is referenced by:  swoer  6457  swoord1  6458  swoord2  6459
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