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Theorem hbal 1411
Description: If  x is not free in  ph, it is not free in  A. y ph. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
hbal.1  |-  ( ph  ->  A. x ph )
Assertion
Ref Expression
hbal  |-  ( A. y ph  ->  A. x A. y ph )

Proof of Theorem hbal
StepHypRef Expression
1 hbal.1 . . 3  |-  ( ph  ->  A. x ph )
21alimi 1389 . 2  |-  ( A. y ph  ->  A. y A. x ph )
3 ax-7 1382 . 2  |-  ( A. y A. x ph  ->  A. x A. y ph )
42, 3syl 14 1  |-  ( A. y ph  ->  A. x A. y ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1287
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-5 1381  ax-7 1382  ax-gen 1383
This theorem is referenced by:  hba2  1488  nfal  1513  aaanh  1523  hbex  1572  pm11.53  1823  euf  1953  hbral  2407
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