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 414	. 2 ⊢ (𝜑 → (𝜓 → ¬ 𝜓))
3	2	pm2.01d 189	1 ⊢ (𝜑 → ¬ 𝜓)

Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 397

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 206  df-an 398

This theorem is referenced by:  efrirr  5658  omlimcl  8578  hartogslem1  9537  cfslb2n  10263  fin23lem41  10347  tskuni  10778  4sqlem18  16895  ramlb  16952  ivthlem2  24969  ivthlem3  24970  cosne0  26038  footne  27974  nsnlplig  29734  unbdqndv1  35384  unbdqndv2  35387  knoppndv  35410  dvrelog2b  40931  sticksstones22  40984  fmtno4prm  46243