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Theorem hbra1 2836
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 2835 . 2  |-  F/ x A. x  e.  A  ph
21nfri 1879 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 1396   A.wral 2804
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795  ax-10 1842  ax-12 1859
This theorem depends on definitions:  df-bi 185  df-ex 1618  df-nf 1622  df-ral 2809
This theorem is referenced by:  mpt2bi123f  30811  hbra2VD  34061  tratrbVD  34062  ssralv2VD  34067  bnj1095  34241  bnj1309  34479
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