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  5604  omlimcl  8506  hartogslem1  9450  cfslb2n  10181  fin23lem41  10265  tskuni  10697  4sqlem18  16924  ramlb  16981  ivthlem2  25429  ivthlem3  25430  cosne0  26506  footne  28805  nsnlplig  30567  unbdqndv1  36784  unbdqndv2  36787  knoppndv  36810  dvrelog2b  42519  sticksstones22  42621  fmtno4prm  48050