Theorem tsbi4 33943

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

Assertion

Ref	Expression
tsbi4	|- ( th -> ( ( -. ph \/ ps ) \/ -. ( ph <-> ps ) ) )

Proof of Theorem tsbi4

Step	Hyp	Ref	Expression
1		tsbi3 33942	. 2 |- ( th -> ( ( ps \/ -. ph ) \/ -. ( ps <-> ph ) ) )
2		orcom 402	. . 3 |- ( ( ps \/ -. ph ) <-> ( -. ph \/ ps ) )
3		bicom 212	. . . 4 |- ( ( ps <-> ph ) <-> ( ph <-> ps ) )
4	3	notbii 310	. . 3 |- ( -. ( ps <-> ph ) <-> -. ( ph <-> ps ) )
5	2, 4	orbi12i 543	. 2 |- ( ( ( ps \/ -. ph ) \/ -. ( ps <-> ph ) ) <-> ( ( -. ph \/ ps ) \/ -. ( ph <-> ps ) ) )
6	1, 5	sylib 208	1 |- ( th -> ( ( -. ph \/ ps ) \/ -. ( ph <-> ps ) ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 196   \/ wo 383

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-or 385

This theorem is referenced by:  tsxo4  33947  mpt2bi123f  33971  mptbi12f  33975  ac6s6  33980