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  5594  omlimcl  8488  hartogslem1  9423  cfslb2n  10151  fin23lem41  10235  tskuni  10666  4sqlem18  16866  ramlb  16923  ivthlem2  25373  ivthlem3  25374  cosne0  26458  footne  28694  nsnlplig  30451  unbdqndv1  36521  unbdqndv2  36524  knoppndv  36547  dvrelog2b  42078  sticksstones22  42180  fmtno4prm  47585