Theorem sb4e 1207

Description: One direction of a simplified definition of substitution that unlike sb4 1227 doesn't require a distinctor antecedent.

Assertion

Ref	Expression
sb4e	|- ([y / x]ph -> A.x(x = y -> E.yph))

Proof of Theorem sb4e

Step	Hyp	Ref	Expression
1		sb1 1180	. 2 |- ([y / x]ph -> E.x(x = y /\ ph))
2		equs5e 1202	. 2 |- (E.x(x = y /\ ph) -> A.x(x = y -> E.yph))
3	1, 2	syl 10	1 |- ([y / x]ph -> A.x(x = y -> E.yph))

Syntax hints:   -> wi 3   /\ wa 223  A.wal 958   = wceq 960  E.wex 984  [wsbc 1174

This theorem is referenced by:  hbsb2e 1209

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 967  ax-11 971  ax-4 977  ax-5o 979  ax-6o 982

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 985  df-sb 1176

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