Theorem pm2.01d 190

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  196  pm2.01da  798  swopo  5560  onssneli  6453  oalimcl  8527  rankcf  10737  prlem934  10993  supsrlem  11071  rpnnen1lem5  12947  rennim  15212  smu01lem  16462  opsrtoslem2  21970  cfinufil  23822  alexsub  23939  ostth3  27556  4cyclusnfrgr  30228  cvnref  32227  pconnconn  35225  untelirr  35702  dfon2lem4  35781  heiborlem10  37821  mod2addne  47369  pgnioedg1  48102  pgnioedg2  48103  pgnioedg3  48104  pgnioedg4  48105  pgnioedg5  48106  lindslinindsimp1  48450