Theorem tsxo2 33945

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

Assertion

Ref	Expression
tsxo2	|- ( th -> ( ( ph \/ ps ) \/ -. ( ph \/_ ps ) ) )

Proof of Theorem tsxo2

Step	Hyp	Ref	Expression
1		tsbi2 33941	. 2 |- ( th -> ( ( ph \/ ps ) \/ ( ph <-> ps ) ) )
2		xnor 1466	. . 3 |- ( ( ph <-> ps ) <-> -. ( ph \/_ ps ) )
3	2	orbi2i 541	. 2 |- ( ( ( ph \/ ps ) \/ ( ph <-> ps ) ) <-> ( ( ph \/ ps ) \/ -. ( ph \/_ ps ) ) )
4	1, 3	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-an 386  df-xor 1465

This theorem is referenced by: (None)