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Theorem sb4a 1937
Description: A version of sb4 2086 that doesn't require a distinctor antecedent. (Contributed by NM, 2-Feb-2007.)
Assertion
Ref Expression
sb4a  |-  ( [ y  /  x ] A. y ph  ->  A. x
( x  =  y  ->  ph ) )

Proof of Theorem sb4a
StepHypRef Expression
1 sb1 1658 . 2  |-  ( [ y  /  x ] A. y ph  ->  E. x
( x  =  y  /\  A. y ph ) )
2 equs5a 1898 . 2  |-  ( E. x ( x  =  y  /\  A. y ph )  ->  A. x
( x  =  y  ->  ph ) )
31, 2syl 16 1  |-  ( [ y  /  x ] A. y ph  ->  A. x
( x  =  y  ->  ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 359   A.wal 1546   E.wex 1547   [wsb 1655
This theorem is referenced by:  sb6f  2072  hbsb2a  2074  hbsb2aNEW7  28878  sb6fNEW7  28966
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-11 1753
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1548  df-nf 1551  df-sb 1656
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