Theorem pm1.4 849

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 848	. 2 ⊢ (𝜑 → (𝜓 ∨ 𝜑))
2		orc 847	. 2 ⊢ (𝜓 → (𝜓 ∨ 𝜑))
3	1, 2	jaoi 837	1 ⊢ ((𝜑 ∨ 𝜓) → (𝜓 ∨ 𝜑))

Syntax hints:   → wi 4   ∨ wo 826

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 827

This theorem is referenced by:  orcom  850  orcoms  852  pm2.3  889  pm2.36  950  pm2.37  951  rb-ax2  1825  nfntOLDOLD  1933  prneimg  4517  orcomdd  34216  rp-fakeanorass  38377  orbi1rVD  39599