Theorem pm2.18da 797

Description: Deduction based on reductio ad absurdum. See pm2.18 128. (Contributed by Mario Carneiro, 9-Feb-2017.)

Hypothesis

Ref	Expression
pm2.18da.1	⊢ ((𝜑 ∧ ¬ 𝜓) → 𝜓)

Assertion

Ref	Expression
pm2.18da	⊢ (𝜑 → 𝜓)

Proof of Theorem pm2.18da

Step	Hyp	Ref	Expression
1		pm2.18da.1	. . 3 ⊢ ((𝜑 ∧ ¬ 𝜓) → 𝜓)
2	1	ex 412	. 2 ⊢ (𝜑 → (¬ 𝜓 → 𝜓))
3	2	pm2.18d 127	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 206  df-an 396

This theorem is referenced by:  fpwwe2lem12  10636  bpos  27176  tocyccntz  32806  mxidlirred  33093  sn-0tie0  41872  infdesc  41945  2pwp1prm  46811