Theorem mt2i 97

Description: Modus tollens inference.

Hypotheses

Ref	Expression
mt2i.1	⊢ χ
mt2i.2	⊢ (φ → (ψ → ¬ χ))

Assertion

Ref	Expression
mt2i	⊢ (φ → ¬ ψ)

Proof of Theorem mt2i

Step	Hyp	Ref	Expression
1		mt2i.1	. 2 ⊢ χ
2		mt2i.2	. . 3 ⊢ (φ → (ψ → ¬ χ))
3	2	con2d 83	. 2 ⊢ (φ → (χ → ¬ ψ))
4	1, 3	mpi 44	1 ⊢ (φ → ¬ ψ)

Syntax hints:  ¬ wn 1   → wi 2

This theorem is referenced by:  ssnlim 2407  eirrv 3449  discrlem3 4715  sqrlem18 4748

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

metamath.org