Theorem sb1 1819

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 1816	. 2 |- ( [ y / x ] ph <-> ( ( x = y -> ph ) /\ E. x ( x = y /\ ph ) ) )
2	1	simprbi 275	1 |- ( [ y / x ] ph -> E. x ( x = y /\ ph ) )

Syntax hints:   -> wi 4   /\ wa 104   E.wex 1545   [wsb 1815

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107

This theorem depends on definitions:  df-bi 117  df-sb 1816

This theorem is referenced by:  sbh  1829  sbiedh  1840  sb4a  1854  sb4e  1858  sbcof2  1863  sb4  1885  sb4or  1886  spsbe  1895  sbidm  1904  sb5rf  1905  bj-sbimedh  16713