Theorem sb4a 1723

Description: A version of sb4 1754 that doesn't require a distinctor antecedent. (Contributed by NM, 2-Feb-2007.)

Assertion

Ref	Expression
sb4a	|- ( [ y / x ] A. y ph -> A. x ( x = y -> ph ) )

Proof of Theorem sb4a

Step	Hyp	Ref	Expression
1		sb1 1690	. 2 |- ( [ y / x ] A. y ph -> E. x ( x = y /\ A. y ph ) )
2		equs5a 1716	. 2 |- ( E. x ( x = y /\ A. y ph ) -> A. x ( x = y -> ph ) )
3	1, 2	syl 14	1 |- ( [ y / x ] A. y ph -> A. x ( x = y -> ph ) )

Syntax hints:   -> wi 4   /\ wa 102   A.wal 1283   E.wex 1422   [wsb 1686

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-gen 1379  ax-ie2 1424  ax-11 1438  ax-ial 1468

This theorem depends on definitions:  df-bi 115  df-sb 1687

This theorem is referenced by:  sb6f  1725  hbsb2a  1728