Theorem pm4.53 513

Description: Theorem *4.53 of [WhiteheadRussell] p. 120. (Contributed by NM, 3-Jan-2005.)

Assertion

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

Proof of Theorem pm4.53

Step	Hyp	Ref	Expression
1		pm4.52 512	. . 3 ⊢ ((𝜑 ∧ ¬ 𝜓) ↔ ¬ (¬ 𝜑 ∨ 𝜓))
2	1	con2bii 347	. 2 ⊢ ((¬ 𝜑 ∨ 𝜓) ↔ ¬ (𝜑 ∧ ¬ 𝜓))
3	2	bicomi 214	1 ⊢ (¬ (𝜑 ∧ ¬ 𝜓) ↔ (¬ 𝜑 ∨ 𝜓))

Syntax hints:  ¬ wn 3   ↔ wb 196   ∨ wo 383   ∧ wa 384

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 197  df-or 385  df-an 386

This theorem is referenced by:  undif3  3888  undif3OLD  3889  itg2addnclem  33461  cdleme32e  35733  undif3VD  39118