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Mirrors > Home > ILE Home > Th. List > exmidfodomrlemeldju | Unicode version |
Description: Lemma for exmidfodomr 7141. A variant of djur 7015. (Contributed by Jim Kingdon, 2-Jul-2022.) |
Ref | Expression |
---|---|
exmidfodomrlemeldju.a | |
exmidfodomrlemeldju.el | ⊔ |
Ref | Expression |
---|---|
exmidfodomrlemeldju | inl inr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exmidfodomrlemeldju.a | . . . . . . . . . 10 | |
2 | 1 | sselda 3128 | . . . . . . . . 9 |
3 | el1o 6386 | . . . . . . . . 9 | |
4 | 2, 3 | sylib 121 | . . . . . . . 8 |
5 | 4 | fveq2d 5474 | . . . . . . 7 inl inl |
6 | 5 | eqeq2d 2169 | . . . . . 6 inl inl |
7 | 6 | biimpd 143 | . . . . 5 inl inl |
8 | 7 | rexlimdva 2574 | . . . 4 inl inl |
9 | 8 | imp 123 | . . 3 inl inl |
10 | 9 | orcd 723 | . 2 inl inl inr |
11 | simpr 109 | . . . . . . . . 9 | |
12 | 11, 3 | sylib 121 | . . . . . . . 8 |
13 | 12 | fveq2d 5474 | . . . . . . 7 inr inr |
14 | 13 | eqeq2d 2169 | . . . . . 6 inr inr |
15 | 14 | biimpd 143 | . . . . 5 inr inr |
16 | 15 | rexlimdva 2574 | . . . 4 inr inr |
17 | 16 | imp 123 | . . 3 inr inr |
18 | 17 | olcd 724 | . 2 inr inl inr |
19 | exmidfodomrlemeldju.el | . . 3 ⊔ | |
20 | djur 7015 | . . 3 ⊔ inl inr | |
21 | 19, 20 | sylib 121 | . 2 inl inr |
22 | 10, 18, 21 | mpjaodan 788 | 1 inl inr |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wo 698 wceq 1335 wcel 2128 wrex 2436 wss 3102 c0 3395 cfv 5172 c1o 6358 ⊔ cdju 6983 inlcinl 6991 inrcinr 6992 |
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-sep 4084 ax-nul 4092 ax-pow 4137 ax-pr 4171 ax-un 4395 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 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-ral 2440 df-rex 2441 df-v 2714 df-sbc 2938 df-dif 3104 df-un 3106 df-in 3108 df-ss 3115 df-nul 3396 df-pw 3546 df-sn 3567 df-pr 3568 df-op 3570 df-uni 3775 df-br 3968 df-opab 4028 df-mpt 4029 df-tr 4065 df-id 4255 df-iord 4328 df-on 4330 df-suc 4333 df-xp 4594 df-rel 4595 df-cnv 4596 df-co 4597 df-dm 4598 df-rn 4599 df-res 4600 df-iota 5137 df-fun 5174 df-fn 5175 df-f 5176 df-f1 5177 df-fo 5178 df-f1o 5179 df-fv 5180 df-1st 6090 df-2nd 6091 df-1o 6365 df-dju 6984 df-inl 6993 df-inr 6994 |
This theorem is referenced by: exmidfodomrlemr 7139 |
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