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Mirrors > Home > ILE Home > Th. List > exmidfodomrlemeldju | Unicode version |
Description: Lemma for exmidfodomr 7181. A variant of djur 7046. (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 3147 | . . . . . . . . 9 |
3 | el1o 6416 | . . . . . . . . 9 | |
4 | 2, 3 | sylib 121 | . . . . . . . 8 |
5 | 4 | fveq2d 5500 | . . . . . . 7 inl inl |
6 | 5 | eqeq2d 2182 | . . . . . 6 inl inl |
7 | 6 | biimpd 143 | . . . . 5 inl inl |
8 | 7 | rexlimdva 2587 | . . . 4 inl inl |
9 | 8 | imp 123 | . . 3 inl inl |
10 | 9 | orcd 728 | . 2 inl inl inr |
11 | simpr 109 | . . . . . . . . 9 | |
12 | 11, 3 | sylib 121 | . . . . . . . 8 |
13 | 12 | fveq2d 5500 | . . . . . . 7 inr inr |
14 | 13 | eqeq2d 2182 | . . . . . 6 inr inr |
15 | 14 | biimpd 143 | . . . . 5 inr inr |
16 | 15 | rexlimdva 2587 | . . . 4 inr inr |
17 | 16 | imp 123 | . . 3 inr inr |
18 | 17 | olcd 729 | . 2 inr inl inr |
19 | exmidfodomrlemeldju.el | . . 3 ⊔ | |
20 | djur 7046 | . . 3 ⊔ inl inr | |
21 | 19, 20 | sylib 121 | . 2 inl inr |
22 | 10, 18, 21 | mpjaodan 793 | 1 inl inr |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wo 703 wceq 1348 wcel 2141 wrex 2449 wss 3121 c0 3414 cfv 5198 c1o 6388 ⊔ cdju 7014 inlcinl 7022 inrcinr 7023 |
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 609 ax-in2 610 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-13 2143 ax-14 2144 ax-ext 2152 ax-sep 4107 ax-nul 4115 ax-pow 4160 ax-pr 4194 ax-un 4418 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-sbc 2956 df-dif 3123 df-un 3125 df-in 3127 df-ss 3134 df-nul 3415 df-pw 3568 df-sn 3589 df-pr 3590 df-op 3592 df-uni 3797 df-br 3990 df-opab 4051 df-mpt 4052 df-tr 4088 df-id 4278 df-iord 4351 df-on 4353 df-suc 4356 df-xp 4617 df-rel 4618 df-cnv 4619 df-co 4620 df-dm 4621 df-rn 4622 df-res 4623 df-iota 5160 df-fun 5200 df-fn 5201 df-f 5202 df-f1 5203 df-fo 5204 df-f1o 5205 df-fv 5206 df-1st 6119 df-2nd 6120 df-1o 6395 df-dju 7015 df-inl 7024 df-inr 7025 |
This theorem is referenced by: exmidfodomrlemr 7179 |
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