Theorem sb4a 1789

Description: A version of sb4 1820 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 1754	. 2 |- ( [ y / x ] A. y ph -> E. x ( x = y /\ A. y ph ) )
2		equs5a 1782	. 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 103   A.wal 1341   E.wex 1480   [wsb 1750

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-gen 1437  ax-ie2 1482  ax-11 1494  ax-ial 1522

This theorem depends on definitions:  df-bi 116  df-sb 1751

This theorem is referenced by:  sb6f  1791  hbsb2a  1794