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Mirrors > Home > ILE Home > Th. List > cnveqi | GIF version |
Description: Equality inference for converse. (Contributed by NM, 23-Dec-2008.) |
Ref | Expression |
---|---|
cnveqi.1 | ⊢ 𝐴 = 𝐵 |
Ref | Expression |
---|---|
cnveqi | ⊢ ◡𝐴 = ◡𝐵 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cnveqi.1 | . 2 ⊢ 𝐴 = 𝐵 | |
2 | cnveq 4610 | . 2 ⊢ (𝐴 = 𝐵 → ◡𝐴 = ◡𝐵) | |
3 | 1, 2 | ax-mp 7 | 1 ⊢ ◡𝐴 = ◡𝐵 |
Colors of variables: wff set class |
Syntax hints: = wceq 1289 ◡ccnv 4437 |
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 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 |
This theorem depends on definitions: df-bi 115 df-nf 1395 df-sb 1693 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-in 3005 df-ss 3012 df-br 3846 df-opab 3900 df-cnv 4446 |
This theorem is referenced by: mptcnv 4834 cnvxp 4850 xp0 4851 imainrect 4876 cnvcnv 4883 mptpreima 4924 co01 4945 coi2 4947 cocnvres 4955 fcoi1 5191 fun11iun 5274 f1ocnvd 5846 cnvoprab 5999 f1od2 6000 mapsncnv 6450 sbthlemi8 6671 caseinj 6778 djuinj 6784 fisumcom2 10828 |
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