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Theorem 19.12 1596
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  |-  ( E. x A. y ph  ->  A. y E. x ph )

Proof of Theorem 19.12
StepHypRef Expression
1 hba1 1474 . . 3  |-  ( A. y ph  ->  A. y A. y ph )
21hbex 1568 . 2  |-  ( E. x A. y ph  ->  A. y E. x A. y ph )
3 ax-4 1441 . . 3  |-  ( A. y ph  ->  ph )
43eximi 1532 . 2  |-  ( E. x A. y ph  ->  E. x ph )
52, 4alrimih 1399 1  |-  ( E. x A. y ph  ->  A. y E. x ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1283   E.wex 1422
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-ial 1468
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  hbexd  1625  nfexd  1686  cbvexdh  1844
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