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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 4163 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 4152 | . 2 | |
2 | opelopabf.1 | . . 3 | |
3 | nfcv 2258 | . . . . 5 | |
4 | opelopabf.x | . . . . 5 | |
5 | 3, 4 | nfsbc 2902 | . . . 4 |
6 | opelopabf.3 | . . . . 5 | |
7 | 6 | sbcbidv 2939 | . . . 4 |
8 | 5, 7 | sbciegf 2912 | . . 3 |
9 | 2, 8 | ax-mp 5 | . 2 |
10 | opelopabf.2 | . . 3 | |
11 | opelopabf.y | . . . 4 | |
12 | opelopabf.4 | . . . 4 | |
13 | 11, 12 | sbciegf 2912 | . . 3 |
14 | 10, 13 | ax-mp 5 | . 2 |
15 | 1, 9, 14 | 3bitri 205 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 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: pofun 4204 fmptco 5554 |
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