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Theorem sb1 1641
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 1639 . 2  |-  ( [ y  /  x ] ph 
<->  ( ( x  =  y  ->  ph )  /\  E. x ( x  =  y  /\  ph )
) )
21simprbi 450 1  |-  ( [ y  /  x ] ph  ->  E. x ( x  =  y  /\  ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358   E.wex 1531   [wsb 1638
This theorem is referenced by:  sb4a  1876  sb4e  1877  sbft  1978  sbied  1989  sb4  2006  sbn  2015  sb5rf  2043  sbiedNEW7  29515  sb4NEW7  29527  sbftNEW7  29531  sbnNEW7  29537  sb5rfNEW7  29563
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-sb 1639
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