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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 5308 | . 2 ⊢ ∅ ∈ V | |
2 | int0el 4983 | . 2 ⊢ (∅ ∈ V → ∩ V = ∅) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ∩ V = ∅ |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1533 ∈ wcel 2098 Vcvv 3461 ∅c0 4322 ∩ cint 4950 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-8 2100 ax-9 2108 ax-ext 2696 ax-nul 5307 |
This theorem depends on definitions: df-bi 206 df-an 395 df-tru 1536 df-fal 1546 df-ex 1774 df-sb 2060 df-clab 2703 df-cleq 2717 df-clel 2802 df-v 3463 df-dif 3947 df-ss 3961 df-nul 4323 df-int 4951 |
This theorem is referenced by: (None) |
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