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Mathbox for Jonathan Ben-Naim |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj60 | Structured version Visualization version Unicode version |
Description: Well-founded recursion, part 1 of 3. The proof has been taken from Chapter 4 of Don Monk's notes on Set Theory. See http://euclid.colorado.edu/~monkd/setth.pdf. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.) |
Ref | Expression |
---|---|
bnj60.1 |
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bnj60.2 |
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bnj60.3 |
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bnj60.4 |
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Ref | Expression |
---|---|
bnj60 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bnj60.1 |
. . . . 5
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2 | bnj60.2 |
. . . . 5
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3 | bnj60.3 |
. . . . 5
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4 | 1, 2, 3 | bnj1497 29881 |
. . . 4
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5 | eqid 2453 |
. . . . . . . 8
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6 | 1, 2, 3, 5 | bnj1311 29845 |
. . . . . . 7
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7 | 6 | 3expia 1211 |
. . . . . 6
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8 | 7 | ralrimiv 2802 |
. . . . 5
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9 | 8 | ralrimiva 2804 |
. . . 4
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10 | biid 240 |
. . . . 5
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11 | biid 240 |
. . . . 5
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12 | 10, 5, 11 | bnj1383 29655 |
. . . 4
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13 | 4, 9, 12 | sylancr 670 |
. . 3
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14 | bnj60.4 |
. . . 4
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15 | 14 | funeqi 5605 |
. . 3
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16 | 13, 15 | sylibr 216 |
. 2
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17 | 1, 2, 3, 14 | bnj1498 29882 |
. 2
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18 | 16, 17 | bnj1422 29661 |
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 1671 ax-4 1684 ax-5 1760 ax-6 1807 ax-7 1853 ax-8 1891 ax-9 1898 ax-10 1917 ax-11 1922 ax-12 1935 ax-13 2093 ax-ext 2433 ax-rep 4518 ax-sep 4528 ax-nul 4537 ax-pow 4584 ax-pr 4642 ax-un 6588 ax-reg 8112 ax-inf2 8151 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3or 987 df-3an 988 df-tru 1449 df-fal 1452 df-ex 1666 df-nf 1670 df-sb 1800 df-eu 2305 df-mo 2306 df-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2583 df-ne 2626 df-ral 2744 df-rex 2745 df-reu 2746 df-rab 2748 df-v 3049 df-sbc 3270 df-csb 3366 df-dif 3409 df-un 3411 df-in 3413 df-ss 3420 df-pss 3422 df-nul 3734 df-if 3884 df-pw 3955 df-sn 3971 df-pr 3973 df-tp 3975 df-op 3977 df-uni 4202 df-iun 4283 df-br 4406 df-opab 4465 df-mpt 4466 df-tr 4501 df-eprel 4748 df-id 4752 df-po 4758 df-so 4759 df-fr 4796 df-we 4798 df-xp 4843 df-rel 4844 df-cnv 4845 df-co 4846 df-dm 4847 df-rn 4848 df-res 4849 df-ima 4850 df-ord 5429 df-on 5430 df-lim 5431 df-suc 5432 df-iota 5549 df-fun 5587 df-fn 5588 df-f 5589 df-f1 5590 df-fo 5591 df-f1o 5592 df-fv 5593 df-om 6698 df-1o 7187 df-bnj17 29504 df-bnj14 29506 df-bnj13 29508 df-bnj15 29510 df-bnj18 29512 df-bnj19 29514 |
This theorem is referenced by: bnj1501 29888 bnj1523 29892 |
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