Theorem pm1.4 875

Description: Axiom *1.4 of [WhiteheadRussell] p. 96. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm1.4	⊢ ((𝜑 ∨ 𝜓) → (𝜓 ∨ 𝜑))

Proof of Theorem pm1.4

Step	Hyp	Ref	Expression
1		olc 874	. 2 ⊢ (𝜑 → (𝜓 ∨ 𝜑))
2		orc 873	. 2 ⊢ (𝜓 → (𝜓 ∨ 𝜑))
3	1, 2	jaoi 863	1 ⊢ ((𝜑 ∨ 𝜓) → (𝜓 ∨ 𝜑))

Syntax hints:   → wi 4   ∨ wo 853

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 208  df-or 854

This theorem is referenced by:  orcom  876  orcoms  878  pm2.3  930  pm2.36  977  pm2.37  978  rb-ax2  1760  prneimg  4792  axprg  5373  cnf2dd  38465  orcomdd  38541  rp-fakeanorass  43964  orbi1rVD  45298  itsclc0yqsol  49262