New Foundations Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > NFE Home > Th. List > undif1 | Unicode version |
Description: Absorption of difference by union. This decomposes a union into two disjoint classes (see disjdif 3622). Theorem 35 of [Suppes] p. 29. (Contributed by NM, 19-May-1998.) |
Ref | Expression |
---|---|
undif1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | undir 3504 | . 2 | |
2 | invdif 3496 | . . 3 | |
3 | 2 | uneq1i 3414 | . 2 |
4 | uncom 3408 | . . . . 5 | |
5 | undifv 3624 | . . . . 5 | |
6 | 4, 5 | eqtri 2373 | . . . 4 |
7 | 6 | ineq2i 3454 | . . 3 |
8 | inv1 3577 | . . 3 | |
9 | 7, 8 | eqtri 2373 | . 2 |
10 | 1, 3, 9 | 3eqtr3i 2381 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wceq 1642 cvv 2859 cdif 3206 cun 3207 cin 3208 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-ne 2518 df-v 2861 df-nin 3211 df-compl 3212 df-in 3213 df-un 3214 df-dif 3215 df-ss 3259 df-nul 3551 |
This theorem is referenced by: undif2 3626 nnsucelrlem4 4427 ssfin 4470 sfinltfin 4535 |
Copyright terms: Public domain | W3C validator |