Theorem andasimint-P3.46b 357

Description: Necessary Condition for (i.e. "If" part of) '∧' Defined in Terms of '→' and '¬'. †

Only this direction is deducible with intuitionist logic.

Assertion

Ref	Expression
andasimint-P3.46b	⊢ ((𝜑 ∧ 𝜓) → ¬ (𝜑 → ¬ 𝜓))

Proof of Theorem andasimint-P3.46b

Step	Hyp	Ref	Expression
1		andasim-P3.46-L1 354	1 ⊢ ((𝜑 ∧ 𝜓) → ¬ (𝜑 → ¬ 𝜓))

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

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-true-D2.4 155

This theorem is referenced by: (None)