Theorem pm1.4 869

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 868	. 2 ⊢ (𝜑 → (𝜓 ∨ 𝜑))
2		orc 867	. 2 ⊢ (𝜓 → (𝜓 ∨ 𝜑))
3	1, 2	jaoi 857	1 ⊢ ((𝜑 ∨ 𝜓) → (𝜓 ∨ 𝜑))

Syntax hints:   → wi 4   ∨ wo 847

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 210  df-or 848

This theorem is referenced by:  orcom  870  orcoms  872  pm2.3  925  pm2.36  970  pm2.37  971  rb-ax2  1761  prneimg  4751  cnf2dd  35935  orcomdd  36011  rp-fakeanorass  40746  orbi1rVD  42082  itsclc0yqsol  45726