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Theorem sb4a 1864
Description: A version of sb4 1993 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 1632 . 2  |-  ( [ y  /  x ] A. y ph  ->  E. x
( x  =  y  /\  A. y ph ) )
2 equs5a 1828 . 2  |-  ( E. x ( x  =  y  /\  A. y ph )  ->  A. x
( x  =  y  ->  ph ) )
31, 2syl 15 1  |-  ( [ y  /  x ] A. y ph  ->  A. x
( x  =  y  ->  ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358   A.wal 1527   E.wex 1528   [wsb 1629
This theorem is referenced by:  sb6f  1979  hbsb2a  1981
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-11 1715
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529  df-nf 1532  df-sb 1630
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