Theorem sb1 1689

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 1686	. 2 |- ( [ y / x ] ph <-> ( ( x = y -> ph ) /\ E. x ( x = y /\ ph ) ) )
2	1	simprbi 269	1 |- ( [ y / x ] ph -> E. x ( x = y /\ ph ) )

Syntax hints:   -> wi 4   /\ wa 102   E.wex 1421   [wsb 1685

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 1686

This theorem is referenced by:  sbh  1699  sbiedh  1710  sb4a  1722  sb4e  1726  sbcof2  1731  sb4  1753  sb4or  1754  spsbe  1763  sbidm  1772  sb5rf  1773  bj-sbimedh  10582