Theorem ts3an1

Description: A Tseitin axiom for triple logical conjunction, in deduction form. (Contributed by Giovanni Mascellani, 25-Mar-2018)

	Ref	Expression
Assertion	ts3an1	|- ( th -> ( ( -. ( ph /\ ps ) \/ -. ch ) \/ ( ph /\ ps /\ ch ) ) )

Proof

Step	Hyp	Ref	Expression
1		tsan1	|- ( th -> ( ( -. ( ph /\ ps ) \/ -. ch ) \/ ( ( ph /\ ps ) /\ ch ) ) )
2		df-3an	|- ( ( ph /\ ps /\ ch ) <-> ( ( ph /\ ps ) /\ ch ) )
3	2	orbi2i	|- ( ( ( -. ( ph /\ ps ) \/ -. ch ) \/ ( ph /\ ps /\ ch ) ) <-> ( ( -. ( ph /\ ps ) \/ -. ch ) \/ ( ( ph /\ ps ) /\ ch ) ) )
4	1 3	sylibr	|- ( th -> ( ( -. ( ph /\ ps ) \/ -. ch ) \/ ( ph /\ ps /\ ch ) ) )