Theorem pm2.01da 798

Description: Deduction based on reductio ad absurdum. See pm2.01 188. (Contributed by Mario Carneiro, 9-Feb-2017.)

Hypothesis

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

Assertion

Ref	Expression
pm2.01da	⊢ (𝜑 → ¬ 𝜓)

Proof of Theorem pm2.01da

Step	Hyp	Ref	Expression
1		pm2.01da.1	. . 3 ⊢ ((𝜑 ∧ 𝜓) → ¬ 𝜓)
2	1	ex 412	. 2 ⊢ (𝜑 → (𝜓 → ¬ 𝜓))
3	2	pm2.01d 190	1 ⊢ (𝜑 → ¬ 𝜓)

Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 395

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

This theorem depends on definitions:  df-bi 207  df-an 396

This theorem is referenced by:  efrirr  5634  omlimcl  8590  hartogslem1  9556  cfslb2n  10282  fin23lem41  10366  tskuni  10797  4sqlem18  16982  ramlb  17039  ivthlem2  25405  ivthlem3  25406  cosne0  26490  footne  28702  nsnlplig  30462  unbdqndv1  36526  unbdqndv2  36529  knoppndv  36552  dvrelog2b  42079  sticksstones22  42181  fmtno4prm  47589