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

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  207  ax6dgen  2169  nlim2  8471  infn0  9258  elirrvOLDOLD  9557  cardom  9968  0nnnALT  12269  nthruz  16305  hauspwdom  23623  fin1aufil  24054  rectbntr0  24955  lgam1  27190  gam1  27191  konigsberg  30545  ex-po  30723  strlem1  32539  eulerpartlemt  34702  nalfal  36799  bj-mt2bi  37045  finxpreclem3  37922  nregmodel  45611  quantgodelALT  47474  tannpoly  47509