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Theorem sb4a 1757
Description: A version of sb4 1788 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 1724 . 2  |-  ( [ y  /  x ] A. y ph  ->  E. x
( x  =  y  /\  A. y ph ) )
2 equs5a 1750 . 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 103   A.wal 1314   E.wex 1453   [wsb 1720
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-gen 1410  ax-ie2 1455  ax-11 1469  ax-ial 1499
This theorem depends on definitions:  df-bi 116  df-sb 1721
This theorem is referenced by:  sb6f  1759  hbsb2a  1762
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