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  5621  omlimcl  8545  hartogslem1  9502  cfslb2n  10228  fin23lem41  10312  tskuni  10743  4sqlem18  16940  ramlb  16997  ivthlem2  25360  ivthlem3  25361  cosne0  26445  footne  28657  nsnlplig  30417  unbdqndv1  36503  unbdqndv2  36506  knoppndv  36529  dvrelog2b  42061  sticksstones22  42163  fmtno4prm  47580