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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 4026 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 4015 | . 2 | |
2 | opelopabf.1 | . . 3 | |
3 | nfcv 2219 | . . . . 5 | |
4 | opelopabf.x | . . . . 5 | |
5 | 3, 4 | nfsbc 2835 | . . . 4 |
6 | opelopabf.3 | . . . . 5 | |
7 | 6 | sbcbidv 2872 | . . . 4 |
8 | 5, 7 | sbciegf 2845 | . . 3 |
9 | 2, 8 | ax-mp 7 | . 2 |
10 | opelopabf.2 | . . 3 | |
11 | opelopabf.y | . . . 4 | |
12 | opelopabf.4 | . . . 4 | |
13 | 11, 12 | sbciegf 2845 | . . 3 |
14 | 10, 13 | ax-mp 7 | . 2 |
15 | 1, 9, 14 | 3bitri 204 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 103 wceq 1284 wnf 1389 wcel 1433 cvv 2601 wsbc 2815 cop 3401 copab 3838 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-pow 3948 ax-pr 3964 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-eu 1944 df-mo 1945 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-rex 2354 df-v 2603 df-sbc 2816 df-un 2977 df-in 2979 df-ss 2986 df-pw 3384 df-sn 3404 df-pr 3405 df-op 3407 df-opab 3840 |
This theorem is referenced by: pofun 4067 fmptco 5351 |
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