Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > unen | Unicode version |
Description: Equinumerosity of union of disjoint sets. Theorem 4 of [Suppes] p. 92. (Contributed by NM, 11-Jun-1998.) (Revised by Mario Carneiro, 26-Apr-2015.) |
Ref | Expression |
---|---|
unen |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bren 6641 | . . 3 | |
2 | bren 6641 | . . 3 | |
3 | eeanv 1904 | . . . 4 | |
4 | vex 2689 | . . . . . . . 8 | |
5 | vex 2689 | . . . . . . . 8 | |
6 | 4, 5 | unex 4362 | . . . . . . 7 |
7 | f1oun 5387 | . . . . . . 7 | |
8 | f1oen3g 6648 | . . . . . . 7 | |
9 | 6, 7, 8 | sylancr 410 | . . . . . 6 |
10 | 9 | ex 114 | . . . . 5 |
11 | 10 | exlimivv 1868 | . . . 4 |
12 | 3, 11 | sylbir 134 | . . 3 |
13 | 1, 2, 12 | syl2anb 289 | . 2 |
14 | 13 | imp 123 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1331 wex 1468 wcel 1480 cvv 2686 cun 3069 cin 3070 c0 3363 class class class wbr 3929 wf1o 5122 cen 6632 |
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-in1 603 ax-in2 604 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-13 1491 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 ax-un 4355 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 df-dif 3073 df-un 3075 df-in 3077 df-ss 3084 df-nul 3364 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-br 3930 df-opab 3990 df-id 4215 df-xp 4545 df-rel 4546 df-cnv 4547 df-co 4548 df-dm 4549 df-rn 4550 df-fun 5125 df-fn 5126 df-f 5127 df-f1 5128 df-fo 5129 df-f1o 5130 df-en 6635 |
This theorem is referenced by: enpr2d 6711 phplem2 6747 fiunsnnn 6775 unsnfi 6807 endjusym 6981 pm54.43 7046 endjudisj 7066 djuen 7067 frecfzennn 10199 unennn 11910 |
Copyright terms: Public domain | W3C validator |