Theorem 3expa

Description: Exportation from triple to double conjunction. (Contributed by NM, 20-Aug-1995) (Revised to shorten 3exp and pm3.2an3 by Wolf Lammen, 22-Jun-2022.)

	Ref	Expression
Hypothesis	3exp.1	|- ( ( ph /\ ps /\ ch ) -> th )
Assertion	3expa	|- ( ( ( ph /\ ps ) /\ ch ) -> th )

Proof

Step	Hyp	Ref	Expression
1		3exp.1	|- ( ( ph /\ ps /\ ch ) -> th )
2		df-3an	|- ( ( ph /\ ps /\ ch ) <-> ( ( ph /\ ps ) /\ ch ) )
3	2 1	sylbir	|- ( ( ( ph /\ ps ) /\ ch ) -> th )