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Theorem 19.45 1589
Description: Theorem 19.45 of [Margaris] p. 90. (Contributed by NM, 12-Mar-1993.)
Hypothesis
Ref Expression
19.45.1  |-  F/ x ph
Assertion
Ref Expression
19.45  |-  ( E. x ( ph  \/  ps )  <->  ( ph  \/  E. x ps ) )

Proof of Theorem 19.45
StepHypRef Expression
1 19.43 1535 . 2  |-  ( E. x ( ph  \/  ps )  <->  ( E. x ph  \/  E. x ps ) )
2 19.45.1 . . . 4  |-  F/ x ph
3219.9 1551 . . 3  |-  ( E. x ph  <->  ph )
43orbi1i 690 . 2  |-  ( ( E. x ph  \/  E. x ps )  <->  ( ph  \/  E. x ps )
)
51, 4bitri 177 1  |-  ( E. x ( ph  \/  ps )  <->  ( ph  \/  E. x ps ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 102    \/ wo 639   F/wnf 1365   E.wex 1397
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-4 1416  ax-ial 1443
This theorem depends on definitions:  df-bi 114  df-nf 1366
This theorem is referenced by:  eeor  1601
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