Theorem pm5.62 1015

Description: Theorem *5.62 of [WhiteheadRussell] p. 125. (Contributed by Roy F. Longton, 21-Jun-2005.)

Assertion

Ref	Expression
pm5.62	⊢ (((𝜑 ∧ 𝜓) ∨ ¬ 𝜓) ↔ (𝜑 ∨ ¬ 𝜓))

Proof of Theorem pm5.62

Step	Hyp	Ref	Expression
1		exmid 891	. 2 ⊢ (𝜓 ∨ ¬ 𝜓)
2		ordir 1003	. 2 ⊢ (((𝜑 ∧ 𝜓) ∨ ¬ 𝜓) ↔ ((𝜑 ∨ ¬ 𝜓) ∧ (𝜓 ∨ ¬ 𝜓)))
3	1, 2	mpbiran2 706	1 ⊢ (((𝜑 ∧ 𝜓) ∨ ¬ 𝜓) ↔ (𝜑 ∨ ¬ 𝜓))

Syntax hints:  ¬ wn 3   ↔ wb 205   ∧ wa 395   ∨ wo 843

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 206  df-an 396  df-or 844

This theorem is referenced by: (None)