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Mathbox for Alan Sare |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > en3lplem1VD | Structured version Visualization version Unicode version |
Description: Virtual deduction proof of en3lplem1 8137. (Contributed by Alan Sare, 24-Oct-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
en3lplem1VD |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | idn1 37012 |
. . . . . . 7
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2 | simp3 1032 |
. . . . . . 7
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3 | 1, 2 | e1a 37074 |
. . . . . 6
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4 | tpid3g 4078 |
. . . . . 6
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5 | 3, 4 | e1a 37074 |
. . . . 5
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6 | idn2 37060 |
. . . . . 6
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7 | eleq2 2538 |
. . . . . . 7
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8 | 7 | biimprd 231 |
. . . . . 6
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9 | 6, 3, 8 | e21 37180 |
. . . . 5
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10 | pm3.2 454 |
. . . . 5
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11 | 5, 9, 10 | e12 37174 |
. . . 4
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12 | elex22 3045 |
. . . 4
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13 | 11, 12 | e2 37078 |
. . 3
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14 | 13 | in2 37052 |
. 2
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15 | 14 | in1 37009 |
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 1677 ax-4 1690 ax-5 1766 ax-6 1813 ax-7 1859 ax-10 1932 ax-11 1937 ax-12 1950 ax-13 2104 ax-ext 2451 |
This theorem depends on definitions: df-bi 190 df-or 377 df-an 378 df-3or 1008 df-3an 1009 df-tru 1455 df-ex 1672 df-nf 1676 df-sb 1806 df-clab 2458 df-cleq 2464 df-clel 2467 df-nfc 2601 df-v 3033 df-un 3395 df-sn 3960 df-pr 3962 df-tp 3964 df-vd1 37008 df-vd2 37016 |
This theorem is referenced by: en3lplem2VD 37303 |
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