Theorem pm1.4 883

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 882	. 2 ⊢ (𝜑 → (𝜓 ∨ 𝜑))
2		orc 881	. 2 ⊢ (𝜓 → (𝜓 ∨ 𝜑))
3	1, 2	jaoi 871	1 ⊢ ((𝜑 ∨ 𝜓) → (𝜓 ∨ 𝜑))

This proof depends on syntax axioms:   → wi 4   ∨ wo 861

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-or 862

This theorem is used by:  orcom  884  orcoms  886  pm2.3  938  pm2.36  985  pm2.37  986  rb-ax2  1786  prneimg  4824  axprg  5413  cnf2dd  38781  orcomdd  38857  rp-fakeanorass  44280  orbi1rVD  45597  itsclc0yqsol  49585