Theorem bianassc

Description: An inference to merge two lists of conjuncts. (Contributed by Peter Mazsa, 24-Sep-2022)

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

Proof

Step	Hyp	Ref	Expression
1		bianass.1	|- ( ph <-> ( ps /\ ch ) )
2	1	bianass	|- ( ( et /\ ph ) <-> ( ( et /\ ps ) /\ ch ) )
3		ancom	|- ( ( et /\ ps ) <-> ( ps /\ et ) )
4	3	anbi1i	|- ( ( ( et /\ ps ) /\ ch ) <-> ( ( ps /\ et ) /\ ch ) )
5	2 4	bitri	|- ( ( et /\ ph ) <-> ( ( ps /\ et ) /\ ch ) )