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Theorem sb4a 1948
Description: A version of sb4 2089 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 1662 . 2  |-  ( [ y  /  x ] A. y ph  ->  E. x
( x  =  y  /\  A. y ph ) )
2 equs5a 1909 . 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 1549   E.wex 1550   [wsb 1658
This theorem is referenced by:  hbsb2a  2093  sb6f  2127  hbsb2aNEW7  29479  sb6fNEW7  29570
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
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554  df-sb 1659
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