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Theorem 19.12vAUX7 28794
Description: Weak version of 19.12 1859 not requiring ax-7 1741. (Contributed by NM, 10-Oct-2017.)
Assertion
Ref Expression
19.12vAUX7  |-  ( E. x A. y ph  ->  A. y E. x ph )
Distinct variable group:    x, y
Allowed substitution hints:    ph( x, y)

Proof of Theorem 19.12vAUX7
StepHypRef Expression
1 hba1 1794 . . 3  |-  ( A. y ph  ->  A. y A. y ph )
21hbexwAUX7 28789 . 2  |-  ( E. x A. y ph  ->  A. y E. x A. y ph )
3 sp 1755 . . 3  |-  ( A. y ph  ->  ph )
43eximi 1582 . 2  |-  ( E. x A. y ph  ->  E. x ph )
52, 4alrimih 1571 1  |-  ( E. x A. y ph  ->  A. y E. x ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1546   E.wex 1547
This theorem is referenced by:  ax12olem2wAUX7  28796
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-11 1753  ax-7v 28782
This theorem depends on definitions:  df-bi 178  df-ex 1548
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