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Mirrors > Home > MPE Home > Th. List > Mathboxes > csbima12gALTVD | Structured version Visualization version Unicode version |
Description: Virtual deduction proof of csbima12gALTOLD 37218.
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.
csbima12gALTOLD 37218 is csbima12gALTVD 37294 without virtual deductions and was
automatically derived from csbima12gALTVD 37294.
|
Ref | Expression |
---|---|
csbima12gALTVD |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | idn1 36944 |
. . . . . . 7
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2 | csbresgOLD 37216 |
. . . . . . 7
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3 | 1, 2 | e1a 37006 |
. . . . . 6
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4 | rneq 5060 |
. . . . . 6
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5 | 3, 4 | e1a 37006 |
. . . . 5
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6 | csbrngOLD 37217 |
. . . . . 6
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7 | 1, 6 | e1a 37006 |
. . . . 5
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8 | eqeq2 2462 |
. . . . . 6
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9 | 8 | biimpd 211 |
. . . . 5
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10 | 5, 7, 9 | e11 37067 |
. . . 4
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11 | df-ima 4847 |
. . . . . 6
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12 | 11 | ax-gen 1669 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
13 | csbeq2gOLD 36916 |
. . . . 5
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14 | 1, 12, 13 | e10 37073 |
. . . 4
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15 | eqeq2 2462 |
. . . . 5
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16 | 15 | biimpd 211 |
. . . 4
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17 | 10, 14, 16 | e11 37067 |
. . 3
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18 | df-ima 4847 |
. . 3
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19 | eqeq2 2462 |
. . . 4
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20 | 19 | biimprcd 229 |
. . 3
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21 | 17, 18, 20 | e10 37073 |
. 2
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22 | 21 | in1 36941 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-9 1896 ax-10 1915 ax-11 1920 ax-12 1933 ax-13 2091 ax-ext 2431 ax-sep 4525 ax-nul 4534 ax-pr 4639 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3an 987 df-tru 1447 df-ex 1664 df-nf 1668 df-sb 1798 df-eu 2303 df-mo 2304 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2581 df-ne 2624 df-rab 2746 df-v 3047 df-sbc 3268 df-csb 3364 df-dif 3407 df-un 3409 df-in 3411 df-ss 3418 df-nul 3732 df-if 3882 df-sn 3969 df-pr 3971 df-op 3975 df-br 4403 df-opab 4462 df-xp 4840 df-cnv 4842 df-dm 4844 df-rn 4845 df-res 4846 df-ima 4847 df-vd1 36940 |
This theorem is referenced by: (None) |
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