Definition df-ex 334

Description: Definition of existential quantifier. Dual of ∀.

Assertion

Ref	Expression
df-ex	⊦ (∃x𝜑 ⧟ ~ ∀x~ 𝜑)

Detailed syntax breakdown of Definition df-ex

Step	Hyp	Ref	Expression
1		wph	. . 3 wff 𝜑
2		vx	. . 3 var x
3	1, 2	wex 319	. 2 wff ∃x𝜑
4	1	wneg 3	. . . 4 wff ~ 𝜑
5	4, 2	wal 318	. . 3 wff ∀x~ 𝜑
6	5	wneg 3	. 2 wff ~ ∀x~ 𝜑
7	3, 6	wlb 55	1 wff (∃x𝜑 ⧟ ~ ∀x~ 𝜑)

This definition is referenced by: (None)