Theorem testable 42546

Description: In classical logic all wffs are testable, that is, it is always true that ( -. ph \/ -. -. ph ). This is not necessarily true in intuitionistic logic. In intuitionistic logic, if this statement is true for some ph, then ph is testable. The proof is trivial because it's simply a special case of the law of the excluded middle, which is true in classical logic but not necessarily true in intuitionisic logic. (Contributed by David A. Wheeler, 5-Dec-2018.)

Assertion

Ref	Expression
testable	|- ( -. ph \/ -. -. ph )

Proof of Theorem testable

Step	Hyp	Ref	Expression
1		exmid 431	1 |- ( -. ph \/ -. -. ph )

Syntax hints:   -. wn 3   \/ 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: (None)