Theorem con3dimp 644

Description: Variant of con3d 640 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 640	. 2 ⊢ (𝜑 → (¬ 𝜒 → ¬ 𝜓))
3	2	imp 124	1 ⊢ ((𝜑 ∧ ¬ 𝜒) → ¬ 𝜓)

This proof depends on syntax axioms:  ¬ wn 3   → wi 4   ∧ wa 104

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-in1 623  ax-in2 624

This theorem is used by:  stoic1a  1476  nelneq  2339  nelneq2  2340  nelss  3309  eqsndc  7210  nnnninf  7466  bcpasc  11206  fiinfnf1o  11227  swrdccat  11509  nnoddn2prmb  13043  pcprod  13127  lgsdir  16166  2lgslem2  16223  2lgs  16235  pw1nct  17045