Theorem wl-alanbii

Description: This theorem extends alanimi to a biconditional. Recurrent usage stacks up more quantifiers. (Contributed by Wolf Lammen, 4-Oct-2019)

	Ref	Expression
Hypothesis	wl-alanbii.1	|- ( ph <-> ( ps /\ ch ) )
Assertion	wl-alanbii	|- ( A. x ph <-> ( A. x ps /\ A. x ch ) )

Proof

Step	Hyp	Ref	Expression
1		wl-alanbii.1	|- ( ph <-> ( ps /\ ch ) )
2	1	albii	|- ( A. x ph <-> A. x ( ps /\ ch ) )
3		19.26	|- ( A. x ( ps /\ ch ) <-> ( A. x ps /\ A. x ch ) )
4	2 3	bitri	|- ( A. x ph <-> ( A. x ps /\ A. x ch ) )