Theorem bnj1101

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

	Ref	Expression
Hypotheses	bnj1101.1	|- E. x ( ph -> ps )
	bnj1101.2	|- ( ch -> ph )
Assertion	bnj1101	|- E. x ( ch -> ps )

Proof

Step	Hyp	Ref	Expression
1		bnj1101.1	|- E. x ( ph -> ps )
2		bnj1101.2	|- ( ch -> ph )
3		pm3.42	|- ( ( ph -> ps ) -> ( ( ch /\ ph ) -> ps ) )
4	1 3	bnj101	|- E. x ( ( ch /\ ph ) -> ps )
5	2	pm4.71i	|- ( ch <-> ( ch /\ ph ) )
6	5	imbi1i	|- ( ( ch -> ps ) <-> ( ( ch /\ ph ) -> ps ) )
7	6	exbii	|- ( E. x ( ch -> ps ) <-> E. x ( ( ch /\ ph ) -> ps ) )
8	4 7	mpbir	|- E. x ( ch -> ps )