Theorem pm2.01d 189

Description: Deduction based on reductio ad absurdum. (Contributed by NM, 18-Aug-1993.) (Proof shortened by Wolf Lammen, 5-Mar-2013.)

Hypothesis

Ref	Expression
pm2.01d.1	⊢ (𝜑 → (𝜓 → ¬ 𝜓))

Assertion

Ref	Expression
pm2.01d	⊢ (𝜑 → ¬ 𝜓)

Proof of Theorem pm2.01d

Step	Hyp	Ref	Expression
1		pm2.01d.1	. 2 ⊢ (𝜑 → (𝜓 → ¬ 𝜓))
2		id 22	. 2 ⊢ (¬ 𝜓 → ¬ 𝜓)
3	1, 2	pm2.61d1 180	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-3 8

This theorem is referenced by:  pm2.65d  195  pm2.01da  797  swopo  5597  onssneli  6484  oalimcl  8582  rankcf  10811  prlem934  11067  supsrlem  11145  rpnnen1lem5  13011  rennim  15239  smu01lem  16480  opsrtoslem2  22065  cfinufil  23920  alexsub  24037  ostth3  27664  4cyclusnfrgr  30222  cvnref  32221  pconnconn  35072  untelirr  35543  dfon2lem4  35623  heiborlem10  37534  lindslinindsimp1  47876