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Theorem sb1 1722
Description: One direction of a simplified definition of substitution. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
sb1  |-  ( [ y  /  x ] ph  ->  E. x ( x  =  y  /\  ph ) )

Proof of Theorem sb1
StepHypRef Expression
1 df-sb 1719 . 2  |-  ( [ y  /  x ] ph 
<->  ( ( x  =  y  ->  ph )  /\  E. x ( x  =  y  /\  ph )
) )
21simprbi 271 1  |-  ( [ y  /  x ] ph  ->  E. x ( x  =  y  /\  ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103   E.wex 1451   [wsb 1718
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106
This theorem depends on definitions:  df-bi 116  df-sb 1719
This theorem is referenced by:  sbh  1732  sbiedh  1743  sb4a  1755  sb4e  1759  sbcof2  1764  sb4  1786  sb4or  1787  spsbe  1796  sbidm  1805  sb5rf  1806  bj-sbimedh  12780
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