Theorem bianass

Description: An inference to merge two lists of conjuncts. (Contributed by Giovanni Mascellani, 23-May-2019)

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

Proof

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