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Theorem 19.3h 1515
Description: A wff may be quantified with a variable not free in it. Theorem 19.3 of [Margaris] p. 89. (Contributed by NM, 5-Aug-1993.) (Revised by NM, 21-May-2007.)
Hypothesis
Ref Expression
19.3h.1  |-  ( ph  ->  A. x ph )
Assertion
Ref Expression
19.3h  |-  ( A. x ph  <->  ph )

Proof of Theorem 19.3h
StepHypRef Expression
1 ax-4 1470 . 2  |-  ( A. x ph  ->  ph )
2 19.3h.1 . 2  |-  ( ph  ->  A. x ph )
31, 2impbii 125 1  |-  ( A. x ph  <->  ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104   A.wal 1312
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia2 106  ax-ia3 107  ax-4 1470
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  19.27h  1522  19.28h  1524  equsalh  1687  2eu4  2068
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