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Mathbox for Jonathan Ben-Naim |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj553 | Structured version Unicode version |
Description: Technical lemma for bnj852 32227. This lemma may no longer be used or have become an indirect lemma of the theorem in question (i.e. a lemma of a lemma... of the theorem). (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.) |
Ref | Expression |
---|---|
bnj553.1 |
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bnj553.2 |
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bnj553.3 |
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bnj553.4 |
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bnj553.5 |
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bnj553.6 |
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bnj553.7 |
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bnj553.8 |
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bnj553.9 |
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bnj553.10 |
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bnj553.11 |
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bnj553.12 |
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Ref | Expression |
---|---|
bnj553 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bnj553.12 |
. . . . 5
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2 | 1 | bnj930 32076 |
. . . 4
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3 | opex 4659 |
. . . . . . 7
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4 | 3 | snid 4008 |
. . . . . 6
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5 | elun2 3627 |
. . . . . 6
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6 | 4, 5 | ax-mp 5 |
. . . . 5
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7 | bnj553.8 |
. . . . 5
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8 | 6, 7 | eleqtrri 2539 |
. . . 4
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9 | funopfv 5835 |
. . . 4
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10 | 2, 8, 9 | mpisyl 18 |
. . 3
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11 | 10 | 3ad2ant1 1009 |
. 2
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12 | fveq2 5794 |
. . . . . 6
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13 | 12 | bnj1113 32092 |
. . . . 5
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14 | bnj553.11 |
. . . . 5
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15 | bnj553.10 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
16 | 13, 14, 15 | 3eqtr4g 2518 |
. . . 4
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17 | 16 | 3ad2ant3 1011 |
. . 3
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18 | bnj553.5 |
. . . . 5
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19 | bnj553.9 |
. . . . 5
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20 | bnj553.4 |
. . . . 5
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21 | 18, 19, 15, 20, 1 | bnj548 32203 |
. . . 4
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22 | 21 | 3adant3 1008 |
. . 3
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23 | fveq2 5794 |
. . . . . 6
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24 | 23 | bnj1113 32092 |
. . . . 5
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25 | bnj553.7 |
. . . . . . 7
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26 | 19, 25 | eqeq12i 2472 |
. . . . . 6
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27 | eqcom 2461 |
. . . . . 6
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28 | 26, 27 | bitri 249 |
. . . . 5
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29 | 24, 28 | sylibr 212 |
. . . 4
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30 | 29 | 3ad2ant3 1011 |
. . 3
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31 | 17, 22, 30 | 3eqtr2rd 2500 |
. 2
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32 | 11, 31 | eqtrd 2493 |
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 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-9 1762 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1954 ax-ext 2431 ax-sep 4516 ax-nul 4524 ax-pr 4634 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3an 967 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-eu 2265 df-mo 2266 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2602 df-ne 2647 df-ral 2801 df-rex 2802 df-rab 2805 df-v 3074 df-sbc 3289 df-dif 3434 df-un 3436 df-in 3438 df-ss 3445 df-nul 3741 df-if 3895 df-sn 3981 df-pr 3983 df-op 3987 df-uni 4195 df-iun 4276 df-br 4396 df-opab 4454 df-id 4739 df-xp 4949 df-rel 4950 df-cnv 4951 df-co 4952 df-dm 4953 df-res 4955 df-iota 5484 df-fun 5523 df-fn 5524 df-fv 5529 |
This theorem is referenced by: bnj557 32207 |
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