Theorem selconj

Description: An inference for selecting one of a list of conjuncts. (Contributed by Giovanni Mascellani, 23-May-2019)

	Ref	Expression
Hypothesis	selconj.1	|- ( ph <-> ( ps /\ ch ) )
Assertion	selconj	|- ( ( et /\ ph ) <-> ( ps /\ ( et /\ ch ) ) )

Proof

Step	Hyp	Ref	Expression
1		selconj.1	|- ( ph <-> ( ps /\ ch ) )
2	1	anbi2i	|- ( ( et /\ ph ) <-> ( et /\ ( ps /\ ch ) ) )
3		an12	|- ( ( ps /\ ( et /\ ch ) ) <-> ( et /\ ( ps /\ ch ) ) )
4	2 3	bitr4i	|- ( ( et /\ ph ) <-> ( ps /\ ( et /\ ch ) ) )