Theorem con3and 428

Description: Variant of con3d 125 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 125	. 2 ⊢ (φ → (¬ χ → ¬ ψ))
3	2	imp 418	1 ⊢ ((φ ∧ ¬ χ) → ¬ ψ)

This proof depends on syntax axioms:  ¬ wn 3   → wi 4   ∧ wa 358

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-an 360

This theorem is used by:  ax12olem1  1927  nelneq  2451  nelneq2  2452