Theorem bnj133

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

	Ref	Expression
Hypotheses	bnj133.1	|- ( ph <-> E. x ps )
	bnj133.2	|- ( ch <-> ps )
Assertion	bnj133	|- ( ph <-> E. x ch )

Proof

Step	Hyp	Ref	Expression
1		bnj133.1	|- ( ph <-> E. x ps )
2		bnj133.2	|- ( ch <-> ps )
3	2	exbii	|- ( E. x ch <-> E. x ps )
4	1 3	bitr4i	|- ( ph <-> E. x ch )