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Mathbox for Alan Sare |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > suctrALT2 | Structured version Visualization version Unicode version |
Description: Virtual deduction proof of suctr 5506. The sucessor of a transitive class is transitive. This proof was generated automatically from the virtual deduction proof suctrALT2VD 37232 using the tools command file translatewithout_overwritingminimize_excludingduplicates.cmd . (Contributed by Alan Sare, 11-Sep-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
suctrALT2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sssucid 5500 |
. . . . 5
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2 | trel 4504 |
. . . . . . 7
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3 | 2 | expd 438 |
. . . . . 6
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4 | 3 | adantrd 470 |
. . . . 5
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5 | ssel 3426 |
. . . . 5
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6 | 1, 4, 5 | ee03 37128 |
. . . 4
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7 | simpl 459 |
. . . . . . 7
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8 | 7 | a1i 11 |
. . . . . 6
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9 | eleq2 2518 |
. . . . . . 7
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10 | 9 | biimpcd 228 |
. . . . . 6
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11 | 8, 10 | syl6 34 |
. . . . 5
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12 | 1, 11, 5 | ee03 37128 |
. . . 4
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13 | simpr 463 |
. . . . . 6
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14 | 13 | a1i 11 |
. . . . 5
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15 | elsuci 5489 |
. . . . 5
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16 | 14, 15 | syl6 34 |
. . . 4
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17 | jao 515 |
. . . 4
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18 | 6, 12, 16, 17 | ee222 36858 |
. . 3
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19 | 18 | alrimivv 1774 |
. 2
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20 | dftr2 4499 |
. 2
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21 | 19, 20 | sylibr 216 |
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-10 1915 ax-11 1920 ax-12 1933 ax-13 2091 ax-ext 2431 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-tru 1447 df-ex 1664 df-nf 1668 df-sb 1798 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2581 df-v 3047 df-un 3409 df-in 3411 df-ss 3418 df-sn 3969 df-uni 4199 df-tr 4498 df-suc 5429 |
This theorem is referenced by: (None) |
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