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Mirrors > Home > MPE Home > Th. List > nfiso | Structured version Visualization version Unicode version |
Description: Bound-variable hypothesis builder for an isomorphism. (Contributed by NM, 17-May-2004.) (Proof shortened by Andrew Salmon, 22-Oct-2011.) |
Ref | Expression |
---|---|
nfiso.1 |
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nfiso.2 |
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nfiso.3 |
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nfiso.4 |
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nfiso.5 |
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Ref | Expression |
---|---|
nfiso |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-isom 5598 |
. 2
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2 | nfiso.1 |
. . . 4
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3 | nfiso.4 |
. . . 4
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4 | nfiso.5 |
. . . 4
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5 | 2, 3, 4 | nff1o 5826 |
. . 3
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6 | nfcv 2612 |
. . . . . . 7
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7 | nfiso.2 |
. . . . . . 7
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8 | nfcv 2612 |
. . . . . . 7
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9 | 6, 7, 8 | nfbr 4440 |
. . . . . 6
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10 | 2, 6 | nffv 5886 |
. . . . . . 7
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11 | nfiso.3 |
. . . . . . 7
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12 | 2, 8 | nffv 5886 |
. . . . . . 7
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13 | 10, 11, 12 | nfbr 4440 |
. . . . . 6
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14 | 9, 13 | nfbi 2037 |
. . . . 5
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15 | 3, 14 | nfral 2789 |
. . . 4
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16 | 3, 15 | nfral 2789 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
17 | 5, 16 | nfan 2031 |
. 2
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18 | 1, 17 | nfxfr 1704 |
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-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-ral 2761 df-rex 2762 df-rab 2765 df-v 3033 df-dif 3393 df-un 3395 df-in 3397 df-ss 3404 df-nul 3723 df-if 3873 df-sn 3960 df-pr 3962 df-op 3966 df-uni 4191 df-br 4396 df-opab 4455 df-rel 4846 df-cnv 4847 df-co 4848 df-dm 4849 df-rn 4850 df-iota 5553 df-fun 5591 df-fn 5592 df-f 5593 df-f1 5594 df-fo 5595 df-f1o 5596 df-fv 5597 df-isom 5598 |
This theorem is referenced by: (None) |
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