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Mirrors > Home > MPE Home > Th. List > Mathboxes > csbsngVD | Structured version Visualization version Unicode version |
Description: Virtual deduction proof of csbsng 4243.
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.
csbsng 4243 is csbsngVD 39129 without virtual deductions and was automatically
derived from csbsngVD 39129.
|
Ref | Expression |
---|---|
csbsngVD |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | idn1 38790 | . . . . . . . . 9 | |
2 | sbceqg 3984 | . . . . . . . . 9 | |
3 | 1, 2 | e1a 38852 | . . . . . . . 8 |
4 | csbconstg 3546 | . . . . . . . . . 10 | |
5 | 1, 4 | e1a 38852 | . . . . . . . . 9 |
6 | eqeq1 2626 | . . . . . . . . 9 | |
7 | 5, 6 | e1a 38852 | . . . . . . . 8 |
8 | bibi1 341 | . . . . . . . . 9 | |
9 | 8 | biimprd 238 | . . . . . . . 8 |
10 | 3, 7, 9 | e11 38913 | . . . . . . 7 |
11 | 10 | gen11 38841 | . . . . . 6 |
12 | abbi 2737 | . . . . . . 7 | |
13 | 12 | biimpi 206 | . . . . . 6 |
14 | 11, 13 | e1a 38852 | . . . . 5 |
15 | csbabgOLD 39050 | . . . . . . 7 | |
16 | 15 | eqcomd 2628 | . . . . . 6 |
17 | 1, 16 | e1a 38852 | . . . . 5 |
18 | eqeq1 2626 | . . . . . 6 | |
19 | 18 | biimpcd 239 | . . . . 5 |
20 | 14, 17, 19 | e11 38913 | . . . 4 |
21 | df-sn 4178 | . . . . . 6 | |
22 | 21 | ax-gen 1722 | . . . . 5 |
23 | csbeq2gOLD 38765 | . . . . 5 | |
24 | 1, 22, 23 | e10 38919 | . . . 4 |
25 | eqeq2 2633 | . . . . 5 | |
26 | 25 | biimpd 219 | . . . 4 |
27 | 20, 24, 26 | e11 38913 | . . 3 |
28 | df-sn 4178 | . . 3 | |
29 | eqeq2 2633 | . . . 4 | |
30 | 29 | biimprcd 240 | . . 3 |
31 | 27, 28, 30 | e10 38919 | . 2 |
32 | 31 | in1 38787 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wal 1481 wceq 1483 wcel 1990 cab 2608 wsbc 3435 csb 3533 csn 4177 |
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-sbc 3436 df-csb 3534 df-sn 4178 df-vd1 38786 |
This theorem is referenced by: (None) |
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