Theorem ral0OLD 4412

Description: Obsolete version of ral0 4408 as of 2-Sep-2024. (Contributed by NM, 20-Oct-2005.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
ral0OLD	⊢ ∀𝑥 ∈ ∅ 𝜑

Proof of Theorem ral0OLD

Step	Hyp	Ref	Expression
1		noel 4232	. . 3 ⊢ ¬ 𝑥 ∈ ∅
2	1	pm2.21i 119	. 2 ⊢ (𝑥 ∈ ∅ → 𝜑)
3	2	rgen 3080	1 ⊢ ∀𝑥 ∈ ∅ 𝜑

Syntax hints:   ∈ wcel 2111  ∀wral 3070  ∅c0 4227

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-ext 2729

This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-sb 2070  df-clab 2736  df-cleq 2750  df-clel 2830  df-ral 3075  df-dif 3863  df-nul 4228

This theorem is referenced by: (None)