Theorem pm2.01da 799

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  5668  omlimcl  8614  hartogslem1  9579  cfslb2n  10305  fin23lem41  10389  tskuni  10820  4sqlem18  16995  ramlb  17052  ivthlem2  25500  ivthlem3  25501  cosne0  26585  footne  28745  nsnlplig  30509  unbdqndv1  36490  unbdqndv2  36493  knoppndv  36516  dvrelog2b  42047  sticksstones22  42149  fmtno4prm  47499