Theorem dmorgbint-P4.26c 458

Description: De Morgan's Law B ( Intuitionist Version ). †

The reverse of this implication cannot be deduced in an intuitionist framework. However, it can be added as an axiom to create an intermediate strength logic.

Assertion

Ref	Expression
dmorgbint-P4.26c	⊢ ((¬ 𝜑 ∨ ¬ 𝜓) → ¬ (𝜑 ∧ 𝜓))

Proof of Theorem dmorgbint-P4.26c

Step	Hyp	Ref	Expression
1		dmorgbrev-L4.4 455	1 ⊢ ((¬ 𝜑 ∨ ¬ 𝜓) → ¬ (𝜑 ∧ 𝜓))

Syntax hints:  ¬ wff-neg 9   → wff-imp 10   ∧ wff-and 132   ∨ wff-or 144

This theorem was proved from axioms:  ax-L1 11  ax-L2 12  ax-L3 13  ax-MP 14

This theorem depends on definitions:  df-bi-D2.1 107  df-and-D2.2 133  df-or-D2.3 145  df-true-D2.4 155

This theorem is referenced by: (None)