Theorem iscnrm3lem3

Description: Lemma for iscnrm3lem4 . (Contributed by Zhi Wang, 4-Sep-2024)

	Ref	Expression
Assertion	iscnrm3lem3	|- ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) <-> ( ( ph /\ ch /\ th ) /\ ps ) )

Proof

Step	Hyp	Ref	Expression
1		anass	|- ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) <-> ( ph /\ ( ps /\ ( ch /\ th ) ) ) )
2		anass	|- ( ( ( ph /\ ( ch /\ th ) ) /\ ps ) <-> ( ph /\ ( ( ch /\ th ) /\ ps ) ) )
3		3anass	|- ( ( ph /\ ch /\ th ) <-> ( ph /\ ( ch /\ th ) ) )
4	3	anbi1i	|- ( ( ( ph /\ ch /\ th ) /\ ps ) <-> ( ( ph /\ ( ch /\ th ) ) /\ ps ) )
5		ancom	|- ( ( ps /\ ( ch /\ th ) ) <-> ( ( ch /\ th ) /\ ps ) )
6	5	anbi2i	|- ( ( ph /\ ( ps /\ ( ch /\ th ) ) ) <-> ( ph /\ ( ( ch /\ th ) /\ ps ) ) )
7	2 4 6	3bitr4ri	|- ( ( ph /\ ( ps /\ ( ch /\ th ) ) ) <-> ( ( ph /\ ch /\ th ) /\ ps ) )
8	1 7	bitri	|- ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) <-> ( ( ph /\ ch /\ th ) /\ ps ) )