Theorem pm4.15 789

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 593	. 2 ⊢ (((𝜓 ∧ 𝜒) → ¬ 𝜑) ↔ (𝜑 → ¬ (𝜓 ∧ 𝜒)))
2		nan 626	. 2 ⊢ ((𝜑 → ¬ (𝜓 ∧ 𝜒)) ↔ ((𝜑 ∧ 𝜓) → ¬ 𝜒))
3	1, 2	bitr2i 174	1 ⊢ (((𝜑 ∧ 𝜓) → ¬ 𝜒) ↔ ((𝜓 ∧ 𝜒) → ¬ 𝜑))

Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 97   ↔ wb 98

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

This theorem depends on definitions:  df-bi 110

This theorem is referenced by: (None)