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

Step	Hyp	Ref	Expression
1		df-sb 1646	. 2 |- ( [ y / x ] ph <-> ( ( x = y -> ph ) /\ E. x ( x = y /\ ph ) ) )
2	1	simprbi 260	1 |- ( [ y / x ] ph -> E. x ( x = y /\ ph ) )

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