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Mirrors > Home > ILE Home > Th. List > opelopabaf | Unicode version |
Description: The law of concretion. Theorem 9.5 of [Quine] p. 61. This version of opelopab 4163 uses bound-variable hypotheses in place of distinct variable conditions." (Contributed by Mario Carneiro, 19-Dec-2013.) (Proof shortened by Mario Carneiro, 18-Nov-2016.) |
Ref | Expression |
---|---|
opelopabaf.x | |
opelopabaf.y | |
opelopabaf.1 | |
opelopabaf.2 | |
opelopabaf.3 |
Ref | Expression |
---|---|
opelopabaf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opelopabsb 4152 | . 2 | |
2 | opelopabaf.1 | . . 3 | |
3 | opelopabaf.2 | . . 3 | |
4 | opelopabaf.x | . . . 4 | |
5 | opelopabaf.y | . . . 4 | |
6 | nfv 1493 | . . . 4 | |
7 | opelopabaf.3 | . . . 4 | |
8 | 4, 5, 6, 7 | sbc2iegf 2951 | . . 3 |
9 | 2, 3, 8 | mp2an 422 | . 2 |
10 | 1, 9 | bitri 183 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1316 wnf 1421 wcel 1465 cvv 2660 wsbc 2882 cop 3500 copab 3958 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-rex 2399 df-v 2662 df-sbc 2883 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-opab 3960 |
This theorem is referenced by: (None) |
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