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Mirrors > Home > MPE Home > Th. List > intv | Structured version Visualization version GIF version |
Description: The intersection of the universal class is empty. (Contributed by NM, 11-Sep-2008.) |
Ref | Expression |
---|---|
intv | ⊢ ∩ V = ∅ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0ex 5203 | . 2 ⊢ ∅ ∈ V | |
2 | int0el 4899 | . 2 ⊢ (∅ ∈ V → ∩ V = ∅) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ∩ V = ∅ |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1533 ∈ wcel 2110 Vcvv 3494 ∅c0 4290 ∩ cint 4868 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1907 ax-6 1966 ax-7 2011 ax-8 2112 ax-9 2120 ax-10 2141 ax-11 2157 ax-12 2173 ax-ext 2793 ax-nul 5202 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-tru 1536 df-ex 1777 df-nf 1781 df-sb 2066 df-clab 2800 df-cleq 2814 df-clel 2893 df-nfc 2963 df-v 3496 df-dif 3938 df-in 3942 df-ss 3951 df-nul 4291 df-int 4869 |
This theorem is referenced by: (None) |
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