Theorem tsbi3

Description: A Tseitin axiom for logical biconditional, in deduction form. (Contributed by Giovanni Mascellani, 24-Mar-2018)

	Ref	Expression
Assertion	tsbi3	|- ( th -> ( ( ph \/ -. ps ) \/ -. ( ph <-> ps ) ) )

Proof

Step	Hyp	Ref	Expression
1		biimpr	|- ( ( ph <-> ps ) -> ( ps -> ph ) )
2		con34b	|- ( ( ps -> ph ) <-> ( -. ph -> -. ps ) )
3		pm2.54	|- ( ( -. ph -> -. ps ) -> ( ph \/ -. ps ) )
4	2 3	sylbi	|- ( ( ps -> ph ) -> ( ph \/ -. ps ) )
5	1 4	syl	|- ( ( ph <-> ps ) -> ( ph \/ -. ps ) )
6	5	con3i	|- ( -. ( ph \/ -. ps ) -> -. ( ph <-> ps ) )
7	6	orri	|- ( ( ph \/ -. ps ) \/ -. ( ph <-> ps ) )
8	7	a1i	|- ( th -> ( ( ph \/ -. ps ) \/ -. ( ph <-> ps ) ) )