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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 4790 | . 2 ⊢ ∅ ∈ V | |
2 | int0el 4508 | . 2 ⊢ (∅ ∈ V → ∩ V = ∅) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ∩ V = ∅ |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1483 ∈ wcel 1990 Vcvv 3200 ∅c0 3915 ∩ cint 4475 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-nul 4789 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-v 3202 df-dif 3577 df-in 3581 df-ss 3588 df-nul 3916 df-int 4476 |
This theorem is referenced by: (None) |
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