Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > xpundi | Unicode version |
Description: Distributive law for cross product over union. Theorem 103 of [Suppes] p. 52. (Contributed by NM, 12-Aug-2004.) |
Ref | Expression |
---|---|
xpundi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-xp 4545 | . 2 | |
2 | df-xp 4545 | . . . 4 | |
3 | df-xp 4545 | . . . 4 | |
4 | 2, 3 | uneq12i 3228 | . . 3 |
5 | elun 3217 | . . . . . . 7 | |
6 | 5 | anbi2i 452 | . . . . . 6 |
7 | andi 807 | . . . . . 6 | |
8 | 6, 7 | bitri 183 | . . . . 5 |
9 | 8 | opabbii 3995 | . . . 4 |
10 | unopab 4007 | . . . 4 | |
11 | 9, 10 | eqtr4i 2163 | . . 3 |
12 | 4, 11 | eqtr4i 2163 | . 2 |
13 | 1, 12 | eqtr4i 2163 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wo 697 wceq 1331 wcel 1480 cun 3069 copab 3988 cxp 4537 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-un 3075 df-opab 3990 df-xp 4545 |
This theorem is referenced by: xpun 4600 djuassen 7073 xpdjuen 7074 |
Copyright terms: Public domain | W3C validator |