Theorem pm2.01da 804

Description: Deduction based on reductio ad absurdum. See pm2.01 189. (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 413	. 2 ⊢ (𝜑 → (𝜓 → ¬ 𝜓))
3	2	pm2.01d 191	1 ⊢ (𝜑 → ¬ 𝜓)

Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 396

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 208  df-an 397

This theorem is referenced by:  efrirr  5598  omlimcl  8503  hartogslem1  9447  cfslb2n  10181  fin23lem41  10265  tskuni  10697  4sqlem18  16924  ramlb  16981  ivthlem2  25437  ivthlem3  25438  cosne0  26511  footne  28809  nsnlplig  30570  unbdqndv1  36814  unbdqndv2  36817  knoppndv  36840  dvrelog2b  42551  sticksstones22  42653  fmtno4prm  48053