Theorem con3dimp 625

Description: Variant of con3d 621 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 621	. 2 ⊢ (𝜑 → (¬ 𝜒 → ¬ 𝜓))
3	2	imp 123	1 ⊢ ((𝜑 ∧ ¬ 𝜒) → ¬ 𝜓)

Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 103

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-in1 604  ax-in2 605

This theorem is referenced by:  nelneq  2266  nelneq2  2267  nelss  3202  nnnninf  7086  bcpasc  10675  fiinfnf1o  10695  nnoddn2prmb  12190  pcprod  12272  lgsdir  13536  pw1nct  13843