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Theorem hbsb2e 2098
Description: Special case of a bound-variable hypothesis builder for substitution. (Contributed by NM, 2-Feb-2007.)
Assertion
Ref Expression
hbsb2e  |-  ( [ y  /  x ] ph  ->  A. x [ y  /  x ] E. y ph )

Proof of Theorem hbsb2e
StepHypRef Expression
1 sb4e 1949 . 2  |-  ( [ y  /  x ] ph  ->  A. x ( x  =  y  ->  E. y ph ) )
2 sb2 2090 . . 3  |-  ( A. x ( x  =  y  ->  E. y ph )  ->  [ y  /  x ] E. y ph )
32a5i 1807 . 2  |-  ( A. x ( x  =  y  ->  E. y ph )  ->  A. x [ y  /  x ] E. y ph )
41, 3syl 16 1  |-  ( [ y  /  x ] ph  ->  A. x [ y  /  x ] E. y ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1549   E.wex 1550   [wsb 1658
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-11 1761  ax-12 1950
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554  df-sb 1659
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