Theorem expandan

Description: Expand conjunction to primitives. (Contributed by Rohan Ridenour, 13-Aug-2023)

	Ref	Expression
Hypotheses	expandan.1	|- ( ph <-> ps )
	expandan.2	|- ( ch <-> th )
Assertion	expandan	|- ( ( ph /\ ch ) <-> -. ( ps -> -. th ) )

Proof

Step	Hyp	Ref	Expression
1		expandan.1	|- ( ph <-> ps )
2		expandan.2	|- ( ch <-> th )
3	1 2	anbi12i	|- ( ( ph /\ ch ) <-> ( ps /\ th ) )
4		df-an	|- ( ( ps /\ th ) <-> -. ( ps -> -. th ) )
5	3 4	bitri	|- ( ( ph /\ ch ) <-> -. ( ps -> -. th ) )