Theorem sb4e

Description: One direction of a simplified definition of substitution that unlike sb4b does not require a distinctor antecedent. Usage of this theorem is discouraged because it depends on ax-13 . (Contributed by NM, 2-Feb-2007) (New usage is discouraged.)

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

Proof

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