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Theorem 19.12 1497
Description: Theorem 19.12 of [Margaris] p. 89. Assuming the converse is a mistake sometimes made by beginners! (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
19.12 (xyφyxφ)

Proof of Theorem 19.12
StepHypRef Expression
1 hba1 1382 . . 3 (yφyyφ)
21hbex 1471 . 2 (xyφyxyφ)
3 ax-4 1349 . . 3 (yφφ)
43eximi 1437 . 2 (xyφxφ)
52, 4alrimih 1304 1 (xyφyxφ)
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1281  wex 1328
This theorem is referenced by:  hbexd  1525  nfexd  1584  cbvexdh  1737
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 97  ax-ia2 98  ax-ia3 99  ax-5 1282  ax-7 1283  ax-gen 1284  ax-ie1 1329  ax-ie2 1330  ax-4 1349  ax-ial 1376
This theorem depends on definitions:  df-bi 108
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