Theorem sb1 1651

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 1649	. 2 |- ([y / x]ph <-> ((x = y -> ph) /\ E.x(x = y /\ ph)))
2	1	simprbi 450	1 |- ([y / x]ph -> E.x(x = y /\ ph))

Syntax hints:   -> wi 4   /\ wa 358  E.wex 1541  [wsb 1648

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360  df-sb 1649

This theorem is referenced by:  sb4a  1923  sb4e  1924  sbft  2025  sbied  2036  sb4  2053  sbn  2062  sb5rf  2090