![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
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 4452 | . 2 ⊢ (A = B → ◡A = ◡B) | |
3 | 1, 2 | ax-mp 7 | 1 ⊢ ◡A = ◡B |
Colors of variables: wff set class |
Syntax hints: = wceq 1242 ◡ccnv 4287 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-in 2918 df-ss 2925 df-br 3756 df-opab 3810 df-cnv 4296 |
This theorem is referenced by: cnvxp 4685 xp0 4686 imainrect 4709 cnvcnv 4716 mptpreima 4757 co01 4778 coi2 4780 fcoi1 5013 fun11iun 5090 f1ocnvd 5644 |
Copyright terms: Public domain | W3C validator |