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Theorem excom13 1576
Description: Swap 1st and 3rd existential quantifiers. (Contributed by NM, 9-Mar-1995.)
Assertion
Ref Expression
excom13 (xyzφzyxφ)

Proof of Theorem excom13
StepHypRef Expression
1 excom 1551 . 2 (xyzφyxzφ)
2 excom 1551 . . 3 (xzφzxφ)
32exbii 1493 . 2 (yxzφyzxφ)
4 excom 1551 . 2 (yzxφzyxφ)
51, 3, 43bitri 195 1 (xyzφzyxφ)
Colors of variables: wff set class
Syntax hints:  wb 98  wex 1378
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-ial 1424
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  exrot3  1577  exrot4  1578  euotd  3982
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