Theorem mt2d 98

Description: Modus tollens deduction.

Hypotheses

Ref	Expression
mt2d.1	⊢ (φ → χ)
mt2d.2	⊢ (φ → (ψ → ¬ χ))

Assertion

Ref	Expression
mt2d	⊢ (φ → ¬ ψ)

Proof of Theorem mt2d

Step	Hyp	Ref	Expression
1		mt2d.1	. 2 ⊢ (φ → χ)
2		mt2d.2	. . 3 ⊢ (φ → (ψ → ¬ χ))
3	2	con2d 83	. 2 ⊢ (φ → (χ → ¬ ψ))
4	1, 3	mpd 46	1 ⊢ (φ → ¬ ψ)

Syntax hints:  ¬ wn 1   → wi 2

This theorem is referenced by:  nn0ltp1let 4556

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

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