Theorem con3and 564

Description: Variant of con3d 561 with importation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.)

Hypothesis

Ref	Expression
con3and.1	⊢ (𝜑 → (𝜓 → 𝜒))

Assertion

Ref	Expression
con3and	⊢ ((𝜑 ∧ ¬ 𝜒) → ¬ 𝜓)

Proof of Theorem con3and

Step	Hyp	Ref	Expression
1		con3and.1	. . 3 ⊢ (𝜑 → (𝜓 → 𝜒))
2	1	con3d 561	. 2 ⊢ (𝜑 → (¬ 𝜒 → ¬ 𝜓))
3	2	imp 115	1 ⊢ ((𝜑 ∧ ¬ 𝜒) → ¬ 𝜓)

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

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-in1 544  ax-in2 545

This theorem is referenced by:  nelneq  2138  nelneq2  2139