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Mirrors > Home > ILE Home > Th. List > opelopabf | Unicode version |
Description: The law of concretion. Theorem 9.5 of [Quine] p. 61. This version of opelopab 4271 uses bound-variable hypotheses in place of distinct variable conditions. (Contributed by NM, 19-Dec-2008.) |
Ref | Expression |
---|---|
opelopabf.x |
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opelopabf.y |
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opelopabf.1 |
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opelopabf.2 |
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opelopabf.3 |
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opelopabf.4 |
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Ref | Expression |
---|---|
opelopabf |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opelopabsb 4260 |
. 2
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2 | opelopabf.1 |
. . 3
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3 | nfcv 2319 |
. . . . 5
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4 | opelopabf.x |
. . . . 5
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5 | 3, 4 | nfsbc 2983 |
. . . 4
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6 | opelopabf.3 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
7 | 6 | sbcbidv 3021 |
. . . 4
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8 | 5, 7 | sbciegf 2994 |
. . 3
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9 | 2, 8 | ax-mp 5 |
. 2
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10 | opelopabf.2 |
. . 3
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11 | opelopabf.y |
. . . 4
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12 | opelopabf.4 |
. . . 4
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13 | 11, 12 | sbciegf 2994 |
. . 3
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14 | 10, 13 | ax-mp 5 |
. 2
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15 | 1, 9, 14 | 3bitri 206 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-14 2151 ax-ext 2159 ax-sep 4121 ax-pow 4174 ax-pr 4209 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-rex 2461 df-v 2739 df-sbc 2963 df-un 3133 df-in 3135 df-ss 3142 df-pw 3577 df-sn 3598 df-pr 3599 df-op 3601 df-opab 4065 |
This theorem is referenced by: pofun 4312 fmptco 5682 |
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