Theorem tsna2 33952

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

Assertion

Ref	Expression
tsna2	|- ( th -> ( ph \/ ( ph -/\ ps ) ) )

Proof of Theorem tsna2

Step	Hyp	Ref	Expression
1		tsan2 33949	. 2 |- ( th -> ( ph \/ -. ( ph /\ ps ) ) )
2		df-nan 1448	. . 3 |- ( ( ph -/\ ps ) <-> -. ( ph /\ ps ) )
3	2	orbi2i 541	. 2 |- ( ( ph \/ ( ph -/\ ps ) ) <-> ( ph \/ -. ( ph /\ ps ) ) )
4	1, 3	sylibr 224	1 |- ( th -> ( ph \/ ( ph -/\ ps ) ) )

Syntax hints:   -. wn 3   -> wi 4   \/ wo 383   /\ wa 384   -/\ wnan 1447

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-nan 1448

This theorem is referenced by: (None)