Theorem sb1 1175

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 1171	. 2 |- ([y / x]ph <-> ((x = y -> ph) /\ E.x(x = y /\ ph)))
2	1	pm3.27bi 326	1 |- ([y / x]ph -> E.x(x = y /\ ph))

Syntax hints:   -> wi 3   /\ wa 223   = wceq 955  E.wex 979  [wsbc 1169

This theorem is referenced by:  sbf 1185  hbs1f 1188  sbied 1194  sb4a 1198  sb4e 1202  sb4 1222  sbn 1230  sb5rf 1258

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 147  df-an 225  df-sb 1171

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