Theorem tsxo3 33946

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

Assertion

Ref	Expression
tsxo3	|- ( th -> ( ( ph \/ -. ps ) \/ ( ph \/_ ps ) ) )

Proof of Theorem tsxo3

Step	Hyp	Ref	Expression
1		tsbi3 33942	. 2 |- ( th -> ( ( ph \/ -. ps ) \/ -. ( ph <-> ps ) ) )
2		df-xor 1465	. . . 4 |- ( ( ph \/_ ps ) <-> -. ( ph <-> ps ) )
3	2	bicomi 214	. . 3 |- ( -. ( ph <-> ps ) <-> ( ph \/_ ps ) )
4	3	orbi2i 541	. 2 |- ( ( ( ph \/ -. ps ) \/ -. ( ph <-> ps ) ) <-> ( ( ph \/ -. ps ) \/ ( ph \/_ ps ) ) )
5	1, 4	sylib 208	1 |- ( th -> ( ( ph \/ -. ps ) \/ ( ph \/_ ps ) ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 196   \/ wo 383   \/_ wxo 1464

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  df-xor 1465

This theorem is referenced by: (None)