Theorem ral0

Description: Vacuous universal quantification is always true. (Contributed by NM, 20-Oct-2005)

	Ref	Expression
Assertion	ral0	$$⊢\forall x\in \varnothing \phi$$

Proof

Step	Hyp	Ref	Expression
1		noel	$$⊢\neg x\in \varnothing$$
2	1	pm2.21i	$$⊢x\in \varnothing \to \phi$$
3	2	rgen	$$⊢\forall x\in \varnothing \phi$$