Theorem pm3.1 484

Description: Theorem *3.1 of [WhiteheadRussell] p. 111. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm3.1	⊢ ((φ ∧ ψ) → ¬ (¬ φ ∨ ¬ ψ))

Proof of Theorem pm3.1

Step	Hyp	Ref	Expression
1		anor 475	. 2 ⊢ ((φ ∧ ψ) ↔ ¬ (¬ φ ∨ ¬ ψ))
2	1	biimpi 186	1 ⊢ ((φ ∧ ψ) → ¬ (¬ φ ∨ ¬ ψ))

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 357   ∧ wa 358

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  df-an 360

This theorem is referenced by:  pm3.14  488