Theorem mt2 203

Description: A rule similar to modus tollens. Inference associated with con2i 140. (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 196	1 ⊢ ¬ 𝜑

This proof depends on syntax axioms:  ¬ wn 3   → wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is used by:  bijust0  207  ax6dgen  2164  nlim2  8502  infn0  9298  elirrvOLDOLD  9597  cardom  10071  0nnnALT  12379  nthruz  16427  hauspwdom  23826  fin1aufil  24257  rectbntr0  25158  lgam1  27397  gam1  27398  konigsberg  30864  ex-po  31042  strlem1  32858  eulerpartlemt  35050  nalfal  37284  bj-mt2bi  37530  finxpreclem3  38410  nregmodel  46101  quantgodelALT  47979  tannpoly  48034