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Theorem 19.12OLD7 29587
Description: Theorem 19.12OLD7 of [Margaris] p. 89. Assuming the converse is a mistake sometimes made by beginners! But sometimes the converse does hold, as in 19.12vvOLD7 29602 and r19.12sn 3864. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
19.12OLD7  |-  ( E. x A. y ph  ->  A. y E. x ph )

Proof of Theorem 19.12OLD7
StepHypRef Expression
1 hba1 1804 . . 3  |-  ( A. y ph  ->  A. y A. y ph )
21hbexOLD7 29586 . 2  |-  ( E. x A. y ph  ->  A. y E. x A. y ph )
3 sp 1763 . . 3  |-  ( A. y ph  ->  ph )
43eximi 1585 . 2  |-  ( E. x A. y ph  ->  E. x ph )
52, 4alrimih 1574 1  |-  ( E. x A. y ph  ->  A. y E. x ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1549   E.wex 1550
This theorem is referenced by:  ax12olem2OLD7  29607
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-11 1761  ax-7OLD7 29579
This theorem depends on definitions:  df-bi 178  df-ex 1551
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