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Theorem 19.12 1628
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 1505 . . 3  |-  ( A. y ph  ->  A. y A. y ph )
21hbex 1600 . 2  |-  ( E. x A. y ph  ->  A. y E. x A. y ph )
3 ax-4 1472 . . 3  |-  ( A. y ph  ->  ph )
43eximi 1564 . 2  |-  ( E. x A. y ph  ->  E. x ph )
52, 4alrimih 1430 1  |-  ( E. x A. y ph  ->  A. y E. x ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1314   E.wex 1453
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-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-4 1472  ax-ial 1499
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  hbexd  1657  nfexd  1719  cbvexdh  1878
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