Theorem inegd 1333

Description: Negation introduction rule from natural deduction. (Contributed by Mario Carneiro, 9-Feb-2017.)

Hypothesis

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

Assertion

Ref	Expression
inegd	⊢ (φ → ¬ ψ)

Proof of Theorem inegd

Step	Hyp	Ref	Expression
1		inegd.1	. . 3 ⊢ ((φ ∧ ψ) → ⊥ )
2	1	ex 423	. 2 ⊢ (φ → (ψ → ⊥ ))
3		dfnot 1332	. 2 ⊢ (¬ ψ ↔ (ψ → ⊥ ))
4	2, 3	sylibr 203	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:  efald  1334