Theorem tsbi2

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

	Ref	Expression
Assertion	tsbi2	|- ( th -> ( ( ph \/ ps ) \/ ( ph <-> ps ) ) )

Proof

Step	Hyp	Ref	Expression
1		pm5.21	|- ( ( -. ph /\ -. ps ) -> ( ph <-> ps ) )
2	1	olcd	|- ( ( -. ph /\ -. ps ) -> ( ( ph \/ ps ) \/ ( ph <-> ps ) ) )
3		pm4.57	|- ( -. ( -. ph /\ -. ps ) <-> ( ph \/ ps ) )
4	3	biimpi	|- ( -. ( -. ph /\ -. ps ) -> ( ph \/ ps ) )
5	4	orcd	|- ( -. ( -. ph /\ -. ps ) -> ( ( ph \/ ps ) \/ ( ph <-> ps ) ) )
6	2 5	pm2.61i	|- ( ( ph \/ ps ) \/ ( ph <-> ps ) )
7	6	a1i	|- ( th -> ( ( ph \/ ps ) \/ ( ph <-> ps ) ) )