Theorem pm2.18da 812

Description: Deduction based on reductio ad absurdum. See pm2.18 129. (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 418	. 2 ⊢ (𝜑 → (¬ 𝜓 → 𝜓))
3	2	pm2.18d 128	1 ⊢ (𝜑 → 𝜓)

This proof depends on syntax axioms:  ¬ wn 3   → wi 4   ∧ wa 401

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402

This theorem is used by:  fpwwe2lem12  10708  bpos  27602  infdesc  27949  tocyccntz  33687  mxidlirred  33979  sn-0tie0  43483  2pwp1prm  48618