Theorem exclmid-P2.12 152

Description: Law of Excluded Middle.

Assertion

Ref	Expression
exclmid-P2.12	⊢ (𝜑 ∨ ¬ 𝜑)

Proof of Theorem exclmid-P2.12

Step	Hyp	Ref	Expression
1		orintr-P2.11b 148	. 2 ⊢ (𝜑 → (𝜑 ∨ ¬ 𝜑))
2		orintl-P2.11a 146	. 2 ⊢ (¬ 𝜑 → (𝜑 ∨ ¬ 𝜑))
3	1, 2	pfbycase-P1.17.2SH 89	1 ⊢ (𝜑 ∨ ¬ 𝜑)

Syntax hints:  ¬ wff-neg 9   ∨ wff-or 144

This theorem was proved from axioms:  ax-L1 11  ax-L2 12  ax-L3 13  ax-MP 14

This theorem depends on definitions:  df-bi-D2.1 107  df-or-D2.3 145

This theorem is referenced by:  ndexclmid-P3.16  181