Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > eliniseg | Unicode version |
Description: Membership in an initial segment. The idiom , meaning , is used to specify an initial segment in (for example) Definition 6.21 of [TakeutiZaring] p. 30. (Contributed by NM, 28-Apr-2004.) (Proof shortened by Andrew Salmon, 27-Aug-2011.) |
Ref | Expression |
---|---|
eliniseg.1 |
Ref | Expression |
---|---|
eliniseg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eliniseg.1 | . 2 | |
2 | elimasng 4713 | . . . 4 | |
3 | df-br 3786 | . . . 4 | |
4 | 2, 3 | syl6bbr 196 | . . 3 |
5 | brcnvg 4534 | . . 3 | |
6 | 4, 5 | bitrd 186 | . 2 |
7 | 1, 6 | mpan2 415 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wcel 1433 cvv 2601 csn 3398 cop 3401 class class class wbr 3785 ccnv 4362 cima 4366 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-pow 3948 ax-pr 3964 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-eu 1944 df-mo 1945 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rex 2354 df-v 2603 df-sbc 2816 df-un 2977 df-in 2979 df-ss 2986 df-pw 3384 df-sn 3404 df-pr 3405 df-op 3407 df-br 3786 df-opab 3840 df-xp 4369 df-cnv 4371 df-dm 4373 df-rn 4374 df-res 4375 df-ima 4376 |
This theorem is referenced by: epini 4716 iniseg 4717 dfco2a 4841 isoini 5477 |
Copyright terms: Public domain | W3C validator |