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Theorem hbsb2a 1981
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 1864 . 2  |-  ( [ y  /  x ] A. y ph  ->  A. x
( x  =  y  ->  ph ) )
2 sb2 1963 . . 3  |-  ( A. x ( x  =  y  ->  ph )  ->  [ y  /  x ] ph )
32a5i 1758 . 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 1527   [wsb 1629
This theorem is referenced by:  hbsb3  1983
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529  df-nf 1532  df-sb 1630
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