Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > djuenun | Unicode version |
Description: Disjoint union is equinumerous to union for disjoint sets. (Contributed by Mario Carneiro, 29-Apr-2015.) (Revised by Jim Kingdon, 19-Aug-2023.) |
Ref | Expression |
---|---|
djuenun | ⊔ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | djuen 7147 | . . 3 ⊔ ⊔ | |
2 | 1 | 3adant3 1002 | . 2 ⊔ ⊔ |
3 | relen 6690 | . . . 4 | |
4 | 3 | brrelex2i 4631 | . . 3 |
5 | 3 | brrelex2i 4631 | . . 3 |
6 | id 19 | . . 3 | |
7 | endjudisj 7146 | . . 3 ⊔ | |
8 | 4, 5, 6, 7 | syl3an 1262 | . 2 ⊔ |
9 | entr 6730 | . 2 ⊔ ⊔ ⊔ ⊔ | |
10 | 2, 8, 9 | syl2anc 409 | 1 ⊔ |
Colors of variables: wff set class |
Syntax hints: wi 4 w3a 963 wceq 1335 wcel 2128 cvv 2712 cun 3100 cin 3101 c0 3394 class class class wbr 3966 cen 6684 ⊔ cdju 6982 |
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 604 ax-in2 605 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-13 2130 ax-14 2131 ax-ext 2139 ax-coll 4080 ax-sep 4083 ax-nul 4091 ax-pow 4136 ax-pr 4170 ax-un 4394 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-fal 1341 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-ne 2328 df-ral 2440 df-rex 2441 df-reu 2442 df-rab 2444 df-v 2714 df-sbc 2938 df-csb 3032 df-dif 3104 df-un 3106 df-in 3108 df-ss 3115 df-nul 3395 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-uni 3774 df-iun 3852 df-br 3967 df-opab 4027 df-mpt 4028 df-tr 4064 df-id 4254 df-iord 4327 df-on 4329 df-suc 4332 df-xp 4593 df-rel 4594 df-cnv 4595 df-co 4596 df-dm 4597 df-rn 4598 df-res 4599 df-ima 4600 df-iota 5136 df-fun 5173 df-fn 5174 df-f 5175 df-f1 5176 df-fo 5177 df-f1o 5178 df-fv 5179 df-1st 6089 df-2nd 6090 df-1o 6364 df-er 6481 df-en 6687 df-dju 6983 df-inl 6992 df-inr 6993 |
This theorem is referenced by: dju1en 7149 djucomen 7152 djuassen 7153 xpdjuen 7154 |
Copyright terms: Public domain | W3C validator |