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Theorem sb1 1691
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 1688 . 2  |-  ( [ y  /  x ] ph 
<->  ( ( x  =  y  ->  ph )  /\  E. x ( x  =  y  /\  ph )
) )
21simprbi 269 1  |-  ( [ y  /  x ] ph  ->  E. x ( x  =  y  /\  ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102   E.wex 1422   [wsb 1687
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105
This theorem depends on definitions:  df-bi 115  df-sb 1688
This theorem is referenced by:  sbh  1701  sbiedh  1712  sb4a  1724  sb4e  1728  sbcof2  1733  sb4  1755  sb4or  1756  spsbe  1765  sbidm  1774  sb5rf  1775  bj-sbimedh  10826
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