Definition df-and-D2.2 133

Description: Definition of Conjunction, '∧'. Read as "and".

Assertion

Ref	Expression
df-and-D2.2	⊢ ((𝜑 ∧ 𝜓) ↔ ¬ (𝜑 → ¬ 𝜓))

Detailed syntax breakdown of Definition df-and-D2.2

Step	Hyp	Ref	Expression
1		wff-ph	. . 3 wff 𝜑
2		wff-ps	. . 3 wff 𝜓
3	1, 2	wff-and 132	. 2 wff (𝜑 ∧ 𝜓)
4	2	wff-neg 9	. . . 4 wff ¬ 𝜓
5	1, 4	wff-imp 10	. . 3 wff (𝜑 → ¬ 𝜓)
6	5	wff-neg 9	. 2 wff ¬ (𝜑 → ¬ 𝜓)
7	3, 6	wff-bi 104	1 wff ((𝜑 ∧ 𝜓) ↔ ¬ (𝜑 → ¬ 𝜓))

This definition is referenced by:  simpl-P2.9a  134  simpr-P2.9b  136  cmb-P2.9c  138