Theorem sb1 1754

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 1751	. 2 |- ( [ y / x ] ph <-> ( ( x = y -> ph ) /\ E. x ( x = y /\ ph ) ) )
2	1	simprbi 273	1 |- ( [ y / x ] ph -> E. x ( x = y /\ ph ) )

Syntax hints:   -> wi 4   /\ wa 103   E.wex 1480   [wsb 1750

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106

This theorem depends on definitions:  df-bi 116  df-sb 1751

This theorem is referenced by:  sbh  1764  sbiedh  1775  sb4a  1789  sb4e  1793  sbcof2  1798  sb4  1820  sb4or  1821  spsbe  1830  sbidm  1839  sb5rf  1840  bj-sbimedh  13662