Theorem pm1.4 645

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 631	. 2 ⊢ (φ → (ψ ∨ φ))
2		orc 632	. 2 ⊢ (ψ → (ψ ∨ φ))
3	1, 2	jaoi 635	1 ⊢ ((φ ∨ ψ) → (ψ ∨ φ))

Syntax hints:   → wi 4   ∨ wo 628

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  orcom  646  orcoms  648  pm2.3  691  pm2.36  716  pm2.37  717  pm2.8  722  dveeq2or  1694  prneimg  3536