Theorem pm1.4 865

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 864	. 2 ⊢ (𝜑 → (𝜓 ∨ 𝜑))
2		orc 863	. 2 ⊢ (𝜓 → (𝜓 ∨ 𝜑))
3	1, 2	jaoi 853	1 ⊢ ((𝜑 ∨ 𝜓) → (𝜓 ∨ 𝜑))

Syntax hints:   → wi 4   ∨ 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 209  df-or 844

This theorem is referenced by:  orcom  866  orcoms  868  pm2.3  921  pm2.36  966  pm2.37  967  rb-ax2  1753  prneimg  4788  cnf2dd  35373  orcomdd  35449  rp-fakeanorass  39885  orbi1rVD  41188  itsclc0yqsol  44758