Theorem pm4.53 1001

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 1000	. . 3 ⊢ ((𝜑 ∧ ¬ 𝜓) ↔ ¬ (¬ 𝜑 ∨ 𝜓))
2	1	con2bii 360	. 2 ⊢ ((¬ 𝜑 ∨ 𝜓) ↔ ¬ (𝜑 ∧ ¬ 𝜓))
3	2	bicomi 227	1 ⊢ (¬ (𝜑 ∧ ¬ 𝜓) ↔ (¬ 𝜑 ∨ 𝜓))

This proof depends on syntax axioms:  ¬ wn 3   ↔ wb 209   ∧ wa 401   ∨ wo 861

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862

This theorem is used by:  undif3  4253  itg2addnclem  38355  cdleme32e  41252  undif3VD  45623