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Theorem hbra1 2811
Description:  x is not free in  A. x  e.  A ph. (Contributed by NM, 18-Oct-1996.) (Proof shortened by Wolf Lammen, 7-Dec-2019.)
Assertion
Ref Expression
hbra1  |-  ( A. x  e.  A  ph  ->  A. x A. x  e.  A  ph )

Proof of Theorem hbra1
StepHypRef Expression
1 nfra1 2810 . 2  |-  F/ x A. x  e.  A  ph
21nfri 1813 1  |-  ( A. x  e.  A  ph  ->  A. x A. x  e.  A  ph )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1368   A.wral 2799
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-12 1794
This theorem depends on definitions:  df-bi 185  df-ex 1588  df-nf 1591  df-ral 2804
This theorem is referenced by:  mpt2bi123f  29124  hbra2VD  31929  tratrbVD  31930  ssralv2VD  31935  bnj1095  32108  bnj1309  32346
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