Theorem an52ds

Description: Inference exchanging the last antecedent with the second. (Contributed by Thierry Arnoux, 3-Jun-2025)

	Ref	Expression
Hypothesis	an52ds.1	|- ( ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) /\ ta ) -> et )
Assertion	an52ds	|- ( ( ( ( ( ph /\ ta ) /\ ch ) /\ th ) /\ ps ) -> et )

Proof

Step	Hyp	Ref	Expression
1		an52ds.1	|- ( ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) /\ ta ) -> et )
2		an32	|- ( ( ( ph /\ ps ) /\ ta ) <-> ( ( ph /\ ta ) /\ ps ) )
3	2	anbi1i	|- ( ( ( ( ph /\ ps ) /\ ta ) /\ th ) <-> ( ( ( ph /\ ta ) /\ ps ) /\ th ) )
4	1	an42ds	|- ( ( ( ( ( ph /\ ps ) /\ ta ) /\ th ) /\ ch ) -> et )
5	3 4	sylanbr	|- ( ( ( ( ( ph /\ ta ) /\ ps ) /\ th ) /\ ch ) -> et )
6	5	an42ds	|- ( ( ( ( ( ph /\ ta ) /\ ch ) /\ th ) /\ ps ) -> et )