Theorem pm1.4 401

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 399	. 2 ⊢ (𝜑 → (𝜓 ∨ 𝜑))
2		orc 400	. 2 ⊢ (𝜓 → (𝜓 ∨ 𝜑))
3	1, 2	jaoi 394	1 ⊢ ((𝜑 ∨ 𝜓) → (𝜓 ∨ 𝜑))

Syntax hints:   → wi 4   ∨ wo 383

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 197  df-or 385

This theorem is referenced by:  orcom  402  orcoms  404  pm2.3  596  pm2.36  888  pm2.37  889  rb-ax2  1678  nfntOLDOLD  1783  prneimg  4388  orcomdd  33891  rp-fakeanorass  37858  orbi1rVD  39083