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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 4008 uses bound-variable hypotheses in place of distinct variable conditions." (Contributed by NM, 19-Dec-2008.) |
Ref | Expression |
---|---|
opelopabf.x | |
opelopabf.y | |
opelopabf.1 | |
opelopabf.2 | |
opelopabf.3 | |
opelopabf.4 |
Ref | Expression |
---|---|
opelopabf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opelopabsb 3997 | . 2 | |
2 | opelopabf.1 | . . 3 | |
3 | nfcv 2178 | . . . . 5 | |
4 | opelopabf.x | . . . . 5 | |
5 | 3, 4 | nfsbc 2784 | . . . 4 |
6 | opelopabf.3 | . . . . 5 | |
7 | 6 | sbcbidv 2817 | . . . 4 |
8 | 5, 7 | sbciegf 2794 | . . 3 |
9 | 2, 8 | ax-mp 7 | . 2 |
10 | opelopabf.2 | . . 3 | |
11 | opelopabf.y | . . . 4 | |
12 | opelopabf.4 | . . . 4 | |
13 | 11, 12 | sbciegf 2794 | . . 3 |
14 | 10, 13 | ax-mp 7 | . 2 |
15 | 1, 9, 14 | 3bitri 195 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 wceq 1243 wnf 1349 wcel 1393 cvv 2557 wsbc 2764 cop 3378 copab 3817 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-pow 3927 ax-pr 3944 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-rex 2312 df-v 2559 df-sbc 2765 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 df-opab 3819 |
This theorem is referenced by: pofun 4049 fmptco 5330 |
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