Theorem pm1.4 679

Description: Axiom *1.4 of [WhiteheadRussell] p. 96. (Contributed by NM, 3-Jan-2005.) (Revised by NM, 15-Nov-2012.)

Assertion

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

Proof of Theorem pm1.4

Step	Hyp	Ref	Expression
1		olc 665	. 2 ⊢ (𝜑 → (𝜓 ∨ 𝜑))
2		orc 666	. 2 ⊢ (𝜓 → (𝜓 ∨ 𝜑))
3	1, 2	jaoi 669	1 ⊢ ((𝜑 ∨ 𝜓) → (𝜓 ∨ 𝜑))

Syntax hints:   → wi 4   ∨ wo 662

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  orcom  680  orcoms  682  pm2.3  725  pm2.36  751  pm2.37  752  pm2.8  757  dveeq2or  1738  prneimg  3574