Theorem bnj1212

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

	Ref	Expression
Hypotheses	bnj1212.1	|- B = { x e. A | ph }
	bnj1212.2	|- ( th <-> ( ch /\ x e. B /\ ta ) )
Assertion	bnj1212	|- ( th -> x e. A )

Proof

Step	Hyp	Ref	Expression
1		bnj1212.1	|- B = { x e. A | ph }
2		bnj1212.2	|- ( th <-> ( ch /\ x e. B /\ ta ) )
3	1	ssrab3	|- B C_ A
4	2	simp2bi	|- ( th -> x e. B )
5	3 4	bnj1213	|- ( th -> x e. A )