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

Step	Hyp	Ref	Expression
1		df-sb 1688	. 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 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