Theorem pm2.18d 103

Description: Deduction based on reductio ad absurdum. (Contributed by FL, 12-Jul-2009.) (Proof shortened by Andrew Salmon, 7-May-2011.)

Hypothesis

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

Assertion

Ref	Expression
pm2.18d	⊢ (φ → ψ)

Proof of Theorem pm2.18d

Step	Hyp	Ref	Expression
1		pm2.18d.1	. 2 ⊢ (φ → (¬ ψ → ψ))
2		pm2.18 102	. 2 ⊢ ((¬ ψ → ψ) → ψ)
3	1, 2	syl 15	1 ⊢ (φ → ψ)

Syntax hints:  ¬ wn 3   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is referenced by:  notnot2  104  pm2.61d  150  pm2.18da  430  oplem1  930  ax10lem4  1941  phi11lem1  4595  0cnelphi  4597