Theorem pm2.18da 430

Description: Deduction based on reductio ad absurdum. (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 423	. 2 ⊢ (φ → (¬ ψ → ψ))
3	2	pm2.18d 103	1 ⊢ (φ → ψ)

Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 358

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 177  df-an 360

This theorem is referenced by: (None)