Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 4231 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 4220 | . 2 | |
2 | opelopabf.1 | . . 3 | |
3 | nfcv 2299 | . . . . 5 | |
4 | opelopabf.x | . . . . 5 | |
5 | 3, 4 | nfsbc 2957 | . . . 4 |
6 | opelopabf.3 | . . . . 5 | |
7 | 6 | sbcbidv 2995 | . . . 4 |
8 | 5, 7 | sbciegf 2968 | . . 3 |
9 | 2, 8 | ax-mp 5 | . 2 |
10 | opelopabf.2 | . . 3 | |
11 | opelopabf.y | . . . 4 | |
12 | opelopabf.4 | . . . 4 | |
13 | 11, 12 | sbciegf 2968 | . . 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 1335 wnf 1440 wcel 2128 cvv 2712 wsbc 2937 cop 3563 copab 4024 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4082 ax-pow 4135 ax-pr 4169 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-rex 2441 df-v 2714 df-sbc 2938 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-opab 4026 |
This theorem is referenced by: pofun 4272 fmptco 5633 |
Copyright terms: Public domain | W3C validator |