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Mathbox for Alan Sare |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > pwtrVD | Structured version Visualization version Unicode version |
Description: Virtual deduction proof of pwtr 4667; see pwtrrVD 37261 for the converse. (Contributed by Alan Sare, 25-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
pwtrVD |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dftr2 4513 |
. . 3
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2 | idn1 36987 |
. . . . . . 7
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3 | idn2 37035 |
. . . . . . . . . 10
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4 | simpr 467 |
. . . . . . . . . 10
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5 | 3, 4 | e2 37053 |
. . . . . . . . 9
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6 | elpwi 3972 |
. . . . . . . . 9
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7 | 5, 6 | e2 37053 |
. . . . . . . 8
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8 | simpl 463 |
. . . . . . . . 9
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9 | 3, 8 | e2 37053 |
. . . . . . . 8
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10 | ssel 3438 |
. . . . . . . 8
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11 | 7, 9, 10 | e22 37093 |
. . . . . . 7
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12 | trss 4520 |
. . . . . . 7
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13 | 2, 11, 12 | e12 37151 |
. . . . . 6
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14 | vex 3060 |
. . . . . . 7
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15 | 14 | elpw 3969 |
. . . . . 6
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16 | 13, 15 | e2bir 37055 |
. . . . 5
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17 | 16 | in2 37027 |
. . . 4
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18 | 17 | gen12 37040 |
. . 3
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19 | biimpr 203 |
. . 3
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20 | 1, 18, 19 | e01 37113 |
. 2
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21 | 20 | in1 36984 |
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 1680 ax-4 1693 ax-5 1769 ax-6 1816 ax-7 1862 ax-10 1926 ax-11 1931 ax-12 1944 ax-13 2102 ax-ext 2442 |
This theorem depends on definitions: df-bi 190 df-an 377 df-tru 1458 df-ex 1675 df-nf 1679 df-sb 1809 df-clab 2449 df-cleq 2455 df-clel 2458 df-nfc 2592 df-ral 2754 df-v 3059 df-in 3423 df-ss 3430 df-pw 3965 df-uni 4213 df-tr 4512 df-vd1 36983 df-vd2 36991 |
This theorem is referenced by: (None) |
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