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Theorem 19.8w 1659
Description: Weak version of 19.8a 1718. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 1-Aug-2017.)
Hypothesis
Ref Expression
19.8w.1  |-  ( ph  ->  A. x ph )
Assertion
Ref Expression
19.8w  |-  ( ph  ->  E. x ph )

Proof of Theorem 19.8w
StepHypRef Expression
1 19.8w.1 . . . . 5  |-  ( ph  ->  A. x ph )
2 notnot 282 . . . . 5  |-  ( ph  <->  -. 
-.  ph )
32albii 1553 . . . . 5  |-  ( A. x ph  <->  A. x  -.  -.  ph )
41, 2, 33imtr3i 256 . . . 4  |-  ( -. 
-.  ph  ->  A. x  -.  -.  ph )
54spnfw 1640 . . 3  |-  ( A. x  -.  ph  ->  -.  ph )
65con2i 112 . 2  |-  ( ph  ->  -.  A. x  -.  ph )
7 df-ex 1529 . 2  |-  ( E. x ph  <->  -.  A. x  -.  ph )
86, 7sylibr 203 1  |-  ( ph  ->  E. x ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1527   E.wex 1528
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-9 1635
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529
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