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Theorem hbsb2a 1729
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 1724 . 2  |-  ( [ y  /  x ] A. y ph  ->  A. x
( x  =  y  ->  ph ) )
2 sb2 1692 . . 3  |-  ( A. x ( x  =  y  ->  ph )  ->  [ y  /  x ] ph )
32a5i 1476 . 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 1283   [wsb 1687
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-11 1438  ax-4 1441  ax-i9 1464  ax-ial 1468
This theorem depends on definitions:  df-bi 115  df-sb 1688
This theorem is referenced by:  hbsb3  1731
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