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Theorem sb4a 1723
Description: A version of sb4 1754 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 1690 . 2  |-  ( [ y  /  x ] A. y ph  ->  E. x
( x  =  y  /\  A. y ph ) )
2 equs5a 1716 . 2  |-  ( E. x ( x  =  y  /\  A. y ph )  ->  A. x
( x  =  y  ->  ph ) )
31, 2syl 14 1  |-  ( [ y  /  x ] A. y ph  ->  A. x
( x  =  y  ->  ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102   A.wal 1283   E.wex 1422   [wsb 1686
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-gen 1379  ax-ie2 1424  ax-11 1438  ax-ial 1468
This theorem depends on definitions:  df-bi 115  df-sb 1687
This theorem is referenced by:  sb6f  1725  hbsb2a  1728
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