Theorem ral0OLD 4516

Description: Obsolete version of ral0 4512 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 4330	. . 3 ⊢ ¬ 𝑥 ∈ ∅
2	1	pm2.21i 119	. 2 ⊢ (𝑥 ∈ ∅ → 𝜑)
3	2	rgen 3063	1 ⊢ ∀𝑥 ∈ ∅ 𝜑

Syntax hints:   ∈ wcel 2106  ∀wral 3061  ∅c0 4322

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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2703

This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1544  df-fal 1554  df-ex 1782  df-sb 2068  df-clab 2710  df-cleq 2724  df-clel 2810  df-ral 3062  df-dif 3951  df-nul 4323

This theorem is referenced by: (None)