Theorem mt2d 615

Description: Modus tollens deduction. (Contributed by NM, 4-Jul-1994.)

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 614	. 2 ⊢ (𝜑 → (𝜒 → ¬ 𝜓))
4	1, 3	mpd 13	1 ⊢ (𝜑 → ¬ 𝜓)

Syntax hints:  ¬ wn 3   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-in1 604  ax-in2 605

This theorem is referenced by:  nsyl3  616  mt2i  634  en2lp  4531  recnz  9284  xnn0dcle  9738  fznuz  10037  uznfz  10038  pcadd  12271  oddennn  12325