Theorem hbsb2e

Description: Special case of a bound-variable hypothesis builder for substitution. 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	hbsb2e	|- ( [ y / x ] ph -> A. x [ y / x ] E. y ph )

Proof

Step	Hyp	Ref	Expression
1		sb4e	|- ( [ y / x ] ph -> A. x ( x = y -> E. y ph ) )
2		sb2	|- ( A. x ( x = y -> E. y ph ) -> [ y / x ] E. y ph )
3	2	axc4i	|- ( A. x ( x = y -> E. y ph ) -> A. x [ y / x ] E. y ph )
4	1 3	syl	|- ( [ y / x ] ph -> A. x [ y / x ] E. y ph )