Theorem pm1.4 699

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 683	. 2 ⊢ (𝜑 → (𝜓 ∨ 𝜑))
2		orc 684	. 2 ⊢ (𝜓 → (𝜓 ∨ 𝜑))
3	1, 2	jaoi 688	1 ⊢ ((𝜑 ∨ 𝜓) → (𝜓 ∨ 𝜑))

Syntax hints:   → wi 4   ∨ wo 680

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  orcom  700  orcoms  702  pm2.3  747  pm2.36  776  pm2.37  777  pm2.8  782  dveeq2or  1770  prneimg  3667