Theorem sb1 1213

Description: One direction of a simplified definition of substitution.

Assertion

Ref	Expression
sb1	|- ([y / x]ph -> E.x(x = y /\ ph))

Proof of Theorem sb1

Step	Hyp	Ref	Expression
1		df-sb 1209	. 2 |- ([y / x]ph <-> ((x = y -> ph) /\ E.x(x = y /\ ph)))
2	1	pm3.27bi 324	1 |- ([y / x]ph -> E.x(x = y /\ ph))

Syntax hints:   -> wi 3   /\ wa 221   = wceq 992  E.wex 1016  [wsbc 1207

This theorem is referenced by:  sbf 1223  hbs1f 1226  sbied 1232  sb4a 1236  sb4e 1240  sb4 1260  sbn 1268  sb5rf 1297

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 145  df-an 223  df-sb 1209

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