Theorem con3dimp 640

Description: Variant of con3d 636 with importation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.)

Hypothesis

Ref	Expression
con3dimp.1	⊢ (𝜑 → (𝜓 → 𝜒))

Assertion

Ref	Expression
con3dimp	⊢ ((𝜑 ∧ ¬ 𝜒) → ¬ 𝜓)

Proof of Theorem con3dimp

Step	Hyp	Ref	Expression
1		con3dimp.1	. . 3 ⊢ (𝜑 → (𝜓 → 𝜒))
2	1	con3d 636	. 2 ⊢ (𝜑 → (¬ 𝜒 → ¬ 𝜓))
3	2	imp 124	1 ⊢ ((𝜑 ∧ ¬ 𝜒) → ¬ 𝜓)

Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-in1 619  ax-in2 620

This theorem is referenced by:  stoic1a  1471  nelneq  2331  nelneq2  2332  nelss  3287  eqsndc  7100  nnnninf  7330  bcpasc  11034  fiinfnf1o  11054  swrdccat  11325  nnoddn2prmb  12858  pcprod  12942  lgsdir  15793  2lgslem2  15850  2lgs  15862  pw1nct  16664