Theorem pm2.01da 429

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

Hypothesis

Ref	Expression
pm2.01da.1	⊢ ((φ ∧ ψ) → ¬ ψ)

Assertion

Ref	Expression
pm2.01da	⊢ (φ → ¬ ψ)

Proof of Theorem pm2.01da

Step	Hyp	Ref	Expression
1		pm2.01da.1	. . 3 ⊢ ((φ ∧ ψ) → ¬ ψ)
2	1	ex 423	. 2 ⊢ (φ → (ψ → ¬ ψ))
3	2	pm2.01d 161	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)