Definition df-bi 189

Description: Definition of ↔, in terms of the other logical connectives.

Assertion

Ref	Expression
df-bi	⊦ ((𝜑 ↔ 𝜓) ⧟ ((𝜑 → 𝜓) ∧ (𝜓 → 𝜑)))

Detailed syntax breakdown of Definition df-bi

Step	Hyp	Ref	Expression
1		wph	. . 3 wff 𝜑
2		wps	. . 3 wff 𝜓
3	1, 2	wbi 188	. 2 wff (𝜑 ↔ 𝜓)
4	1, 2	wim 180	. . 3 wff (𝜑 → 𝜓)
5	2, 1	wim 180	. . 3 wff (𝜓 → 𝜑)
6	4, 5	wand 182	. 2 wff ((𝜑 → 𝜓) ∧ (𝜓 → 𝜑))
7	3, 6	wlb 55	1 wff ((𝜑 ↔ 𝜓) ⧟ ((𝜑 → 𝜓) ∧ (𝜓 → 𝜑)))

This definition is referenced by: (None)