Theorem tsbi1

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

	Ref	Expression
Assertion	tsbi1	|- ( th -> ( ( -. ph \/ -. ps ) \/ ( ph <-> ps ) ) )

Proof

Step	Hyp	Ref	Expression
1		pm5.1	|- ( ( ph /\ ps ) -> ( ph <-> ps ) )
2	1	olcd	|- ( ( ph /\ ps ) -> ( ( -. ph \/ -. ps ) \/ ( ph <-> ps ) ) )
3		pm3.13	|- ( -. ( ph /\ ps ) -> ( -. ph \/ -. ps ) )
4	3	orcd	|- ( -. ( ph /\ ps ) -> ( ( -. ph \/ -. ps ) \/ ( ph <-> ps ) ) )
5	2 4	pm2.61i	|- ( ( -. ph \/ -. ps ) \/ ( ph <-> ps ) )
6	5	a1i	|- ( th -> ( ( -. ph \/ -. ps ) \/ ( ph <-> ps ) ) )