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Mirrors > Home > MPE Home > Th. List > Mathboxes > sucidVD | Structured version Visualization version Unicode version |
Description: A set belongs to its successor. The following User's Proof is a
Virtual Deduction proof completed automatically by the tools
program completeusersproof.cmd, which invokes Mel L. O'Cat's mmj2
and Norm Megill's Metamath Proof Assistant.
sucid 5804 is sucidVD 39108 without virtual deductions and was automatically
derived from sucidVD 39108.
|
Ref | Expression |
---|---|
sucidVD.1 |
Ref | Expression |
---|---|
sucidVD |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sucidVD.1 | . . . 4 | |
2 | 1 | snid 4208 | . . 3 |
3 | elun2 3781 | . . 3 | |
4 | 2, 3 | e0a 38999 | . 2 |
5 | df-suc 5729 | . 2 | |
6 | 4, 5 | eleqtrri 2700 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wcel 1990 cvv 3200 cun 3572 csn 4177 csuc 5725 |
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 |
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-un 3579 df-in 3581 df-ss 3588 df-sn 4178 df-suc 5729 |
This theorem is referenced by: (None) |
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