Theorem mt2 200

Description: A rule similar to modus tollens. Inference associated with con2i 139. (Contributed by NM, 19-Aug-1993.) (Proof shortened by Wolf Lammen, 10-Sep-2013.)

Hypotheses

Ref	Expression
mt2.1	⊢ 𝜓
mt2.2	⊢ (𝜑 → ¬ 𝜓)

Assertion

Ref	Expression
mt2	⊢ ¬ 𝜑

Proof of Theorem mt2

Step	Hyp	Ref	Expression
1		mt2.1	. . 3 ⊢ 𝜓
2	1	a1i 11	. 2 ⊢ (𝜑 → 𝜓)
3		mt2.2	. 2 ⊢ (𝜑 → ¬ 𝜓)
4	2, 3	pm2.65i 194	1 ⊢ ¬ 𝜑

Syntax hints:  ¬ wn 3   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is referenced by:  bijust0  204  ax6dgen  2128  nlim2  8546  infn0  9368  elirrv  9665  cardom  10055  0nnnALT  12330  nthruz  16301  hauspwdom  23530  fin1aufil  23961  rectbntr0  24873  lgam1  27125  gam1  27126  konigsberg  30289  ex-po  30467  strlem1  32282  eulerpartlemt  34336  nalfal  36369  bj-mt2bi  36534  finxpreclem3  37359