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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj1534 | Unicode version |
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.) |
Ref | Expression |
---|---|
bnj1534.1 |
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bnj1534.2 |
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Ref | Expression |
---|---|
bnj1534 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bnj1534.1 |
. 2
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2 | nfcv 2540 |
. . 3
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3 | nfcv 2540 |
. . 3
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4 | nfv 1626 |
. . 3
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5 | bnj1534.2 |
. . . . . 6
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6 | 5 | nfcii 2531 |
. . . . 5
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7 | nfcv 2540 |
. . . . 5
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8 | 6, 7 | nffv 5694 |
. . . 4
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9 | nfcv 2540 |
. . . 4
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10 | 8, 9 | nfne 2658 |
. . 3
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11 | fveq2 5687 |
. . . 4
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12 | fveq2 5687 |
. . . 4
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13 | 11, 12 | neeq12d 2582 |
. . 3
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14 | 2, 3, 4, 10, 13 | cbvrab 2914 |
. 2
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15 | 1, 14 | eqtri 2424 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem is referenced by: bnj1523 29146 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1552 ax-5 1563 ax-17 1623 ax-9 1662 ax-8 1683 ax-6 1740 ax-7 1745 ax-11 1757 ax-12 1946 ax-ext 2385 |
This theorem depends on definitions: df-bi 178 df-or 360 df-an 361 df-3an 938 df-tru 1325 df-ex 1548 df-nf 1551 df-sb 1656 df-clab 2391 df-cleq 2397 df-clel 2400 df-nfc 2529 df-ne 2569 df-ral 2671 df-rex 2672 df-rab 2675 df-v 2918 df-dif 3283 df-un 3285 df-in 3287 df-ss 3294 df-nul 3589 df-if 3700 df-sn 3780 df-pr 3781 df-op 3783 df-uni 3976 df-br 4173 df-iota 5377 df-fv 5421 |
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