Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > zfpair2 | Unicode version |
Description: Derive the abbreviated version of the Axiom of Pairing from ax-pr 3944. (Contributed by NM, 14-Nov-2006.) |
Ref | Expression |
---|---|
zfpair2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-pr 3944 | . . . 4 | |
2 | 1 | bm1.3ii 3878 | . . 3 |
3 | dfcleq 2034 | . . . . 5 | |
4 | vex 2560 | . . . . . . . 8 | |
5 | 4 | elpr 3396 | . . . . . . 7 |
6 | 5 | bibi2i 216 | . . . . . 6 |
7 | 6 | albii 1359 | . . . . 5 |
8 | 3, 7 | bitri 173 | . . . 4 |
9 | 8 | exbii 1496 | . . 3 |
10 | 2, 9 | mpbir 134 | . 2 |
11 | 10 | issetri 2564 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 98 wo 629 wal 1241 wceq 1243 wex 1381 wcel 1393 cvv 2557 cpr 3376 |
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-pr 3944 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 df-un 2922 df-sn 3381 df-pr 3382 |
This theorem is referenced by: prexgOLD 3946 prexg 3947 onintexmid 4297 funopg 4934 |
Copyright terms: Public domain | W3C validator |