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Theorem hbra1 2440
Description:  x is not free in  A. x  e.  A ph. (Contributed by NM, 18-Oct-1996.)
Assertion
Ref Expression
hbra1  |-  ( A. x  e.  A  ph  ->  A. x A. x  e.  A  ph )

Proof of Theorem hbra1
StepHypRef Expression
1 df-ral 2396 . 2  |-  ( A. x  e.  A  ph  <->  A. x
( x  e.  A  ->  ph ) )
2 hba1 1503 . 2  |-  ( A. x ( x  e.  A  ->  ph )  ->  A. x A. x ( x  e.  A  ->  ph ) )
31, 2hbxfrbi 1431 1  |-  ( A. x  e.  A  ph  ->  A. x A. x  e.  A  ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1312    e. wcel 1463   A.wral 2391
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1406  ax-gen 1408  ax-ial 1497
This theorem depends on definitions:  df-bi 116  df-ral 2396
This theorem is referenced by: (None)
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