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Theorem 19.12 1766
Description: Theorem 19.12 of [Margaris] p. 89. Assuming the converse is a mistake sometimes made by beginners! But sometimes the converse does hold, as in 19.12vv 2032 and r19.12sn 3670. (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 nfa1 1719 . . 3  |-  F/ y A. y ph
21nfex 1733 . 2  |-  F/ y E. x A. y ph
3 ax-4 1692 . . 3  |-  ( A. y ph  ->  ph )
43eximi 1574 . 2  |-  ( E. x A. y ph  ->  E. x ph )
52, 4alrimi 1706 1  |-  ( E. x A. y ph  ->  A. y E. x ph )
Colors of variables: wff set class
Syntax hints:    -> wi 6   A.wal 1532   E.wex 1537
This theorem is referenced by:  pm11.61  26959
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-4 1692
This theorem depends on definitions:  df-bi 179  df-tru 1315  df-ex 1538  df-nf 1540
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