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Theorem hbsb2a 1994
Description: Special case of a bound-variable hypothesis builder for substitution. (Contributed by NM, 2-Feb-2007.)
Assertion
Ref Expression
hbsb2a  |-  ( [ y  /  x ] A. y ph  ->  A. x [ y  /  x ] ph )

Proof of Theorem hbsb2a
StepHypRef Expression
1 sb4a 1876 . 2  |-  ( [ y  /  x ] A. y ph  ->  A. x
( x  =  y  ->  ph ) )
2 sb2 1976 . . 3  |-  ( A. x ( x  =  y  ->  ph )  ->  [ y  /  x ] ph )
32a5i 1770 . 2  |-  ( A. x ( x  =  y  ->  ph )  ->  A. x [ y  /  x ] ph )
41, 3syl 15 1  |-  ( [ y  /  x ] A. y ph  ->  A. x [ y  /  x ] ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1530   [wsb 1638
This theorem is referenced by:  hbsb3  1996
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532  df-nf 1535  df-sb 1639
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