Theorem con3dimp 638

Description: Variant of con3d 634 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 634	. 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 617  ax-in2 618

This theorem is referenced by:  stoic1a  1469  nelneq  2330  nelneq2  2331  nelss  3285  eqsndc  7081  nnnninf  7309  bcpasc  11005  fiinfnf1o  11025  swrdccat  11288  nnoddn2prmb  12806  pcprod  12890  lgsdir  15735  2lgslem2  15792  2lgs  15804  pw1nct  16482