Theorem pm1.4 375

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 373	. 2 ⊢ (φ → (ψ ∨ φ))
2		orc 374	. 2 ⊢ (ψ → (ψ ∨ φ))
3	1, 2	jaoi 368	1 ⊢ ((φ ∨ ψ) → (ψ ∨ φ))

Syntax hints:   → wi 4   ∨ wo 357

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 177  df-or 359

This theorem is referenced by:  orcom  376  orcoms  378  pm2.3  555  pm2.36  816  pm2.37  817  rb-ax2  1518