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Theorem hbsb2a 1735
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 1730 . 2  |-  ( [ y  /  x ] A. y ph  ->  A. x
( x  =  y  ->  ph ) )
2 sb2 1698 . . 3  |-  ( A. x ( x  =  y  ->  ph )  ->  [ y  /  x ] ph )
32a5i 1481 . 2  |-  ( A. x ( x  =  y  ->  ph )  ->  A. x [ y  /  x ] ph )
41, 3syl 14 1  |-  ( [ y  /  x ] A. y ph  ->  A. x [ y  /  x ] ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1288   [wsb 1693
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1382  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-11 1443  ax-4 1446  ax-i9 1469  ax-ial 1473
This theorem depends on definitions:  df-bi 116  df-sb 1694
This theorem is referenced by:  hbsb3  1737
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