Theorem pm4.15 564

Description: Theorem *4.15 of [WhiteheadRussell] p. 117. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 18-Nov-2012.)

Assertion

Ref	Expression
pm4.15	⊢ (((φ ∧ ψ) → ¬ χ) ↔ ((ψ ∧ χ) → ¬ φ))

Proof of Theorem pm4.15

Step	Hyp	Ref	Expression
1		con2b 324	. 2 ⊢ (((ψ ∧ χ) → ¬ φ) ↔ (φ → ¬ (ψ ∧ χ)))
2		nan 563	. 2 ⊢ ((φ → ¬ (ψ ∧ χ)) ↔ ((φ ∧ ψ) → ¬ χ))
3	1, 2	bitr2i 241	1 ⊢ (((φ ∧ ψ) → ¬ χ) ↔ ((ψ ∧ χ) → ¬ φ))

Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 176   ∧ 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-an 360

This theorem is referenced by: (None)