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Mirrors > Home > ILE Home > Th. List > elcnv2 | Unicode version |
Description: Membership in a converse. Equation 5 of [Suppes] p. 62. (Contributed by NM, 11-Aug-2004.) |
Ref | Expression |
---|---|
elcnv2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elcnv 4764 | . 2 | |
2 | df-br 3967 | . . . 4 | |
3 | 2 | anbi2i 453 | . . 3 |
4 | 3 | 2exbii 1586 | . 2 |
5 | 1, 4 | bitri 183 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 wceq 1335 wex 1472 wcel 2128 cop 3563 class class class wbr 3966 ccnv 4586 |
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-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-14 2131 ax-ext 2139 ax-sep 4083 ax-pow 4136 ax-pr 4170 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-br 3967 df-opab 4027 df-cnv 4595 |
This theorem is referenced by: cnvuni 4773 |
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