Theorem mt2d 630

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 629	. 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 619  ax-in2 620

This theorem is referenced by:  nsyl3  631  mt2i  649  en2lp  4652  recnz  9573  xnn0dcle  10037  fznuz  10337  uznfz  10338  nninfctlemfo  12616  pcadd  12918  oddennn  13018  perfectlem1  15729  lgseisenlem1  15805