Theorem exmid 404

Description: Law of excluded middle, also called the principle of tertium non datur. Theorem *2.11 of [WhiteheadRussell] p. 101. It says that something is either true or not true; there are no in-between values of truth. This is an essential distinction of our classical logic and is not a theorem of intuitionistic logic. (Contributed by NM, 5-Aug-1993.)

Assertion

Ref	Expression
exmid	⊢ (φ ∨ ¬ φ)

Proof of Theorem exmid

Step	Hyp	Ref	Expression
1		id 19	. 2 ⊢ (¬ φ → ¬ φ)
2	1	orri 365	1 ⊢ (φ ∨ ¬ φ)

Syntax hints:  ¬ wn 3   ∨ wo 357

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 177  df-or 359

This theorem is referenced by:  exmidd  405  pm5.62  889  pm5.63  890  pm4.83  895  4exmid  905  exmidne  2523  rabxm  3574  elimif  3692