Theorem efald 1334

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

Hypothesis

Ref	Expression
efald.1	⊢ ((φ ∧ ¬ ψ) → ⊥ )

Assertion

Ref	Expression
efald	⊢ (φ → ψ)

Proof of Theorem efald

Step	Hyp	Ref	Expression
1		efald.1	. . 3 ⊢ ((φ ∧ ¬ ψ) → ⊥ )
2	1	inegd 1333	. 2 ⊢ (φ → ¬ ¬ ψ)
3	2	notnotrd 105	1 ⊢ (φ → ψ)

Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 358   ⊥ wfal 1317

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  df-tru 1319  df-fal 1320

This theorem is referenced by: (None)