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Theorem sb1 1649
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 1646 . 2  |-  ( [ y  /  x ] ph 
<->  ( ( x  =  y  ->  ph )  /\  E. x ( x  =  y  /\  ph )
) )
21simprbi 260 1  |-  ( [ y  /  x ] ph  ->  E. x ( x  =  y  /\  ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 97   E.wex 1381   [wsb 1645
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100
This theorem depends on definitions:  df-bi 110  df-sb 1646
This theorem is referenced by:  sbh  1659  sbiedh  1670  sb4a  1682  sb4e  1686  sbcof2  1691  sb4  1713  sb4or  1714  spsbe  1723  sbidm  1731  sb5rf  1732  bj-sbimedh  9911
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