Theorem pm4.53r 804

Description: One direction of theorem *4.53 of [WhiteheadRussell] p. 120. The converse also holds in classical logic. (Contributed by Jim Kingdon, 27-Jul-2018.)

Assertion

Ref	Expression
pm4.53r	⊢ ((¬ 𝜑 ∨ 𝜓) → ¬ (𝜑 ∧ ¬ 𝜓))

Proof of Theorem pm4.53r

Step	Hyp	Ref	Expression
1		pm4.52im 803	. 2 ⊢ ((𝜑 ∧ ¬ 𝜓) → ¬ (¬ 𝜑 ∨ 𝜓))
2	1	con2i 557	1 ⊢ ((¬ 𝜑 ∨ 𝜓) → ¬ (𝜑 ∧ ¬ 𝜓))

Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 97   ∨ wo 629

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-in1 544  ax-in2 545  ax-io 630

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  undif3ss  3198