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Mirrors > Home > ILE Home > Th. List > cocnvcnv2 | Unicode version |
Description: A composition is not affected by a double converse of its second argument. (Contributed by NM, 8-Oct-2007.) |
Ref | Expression |
---|---|
cocnvcnv2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cnvcnv2 4717 |
. . 3
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2 | 1 | coeq2i 4439 |
. 2
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3 | resco 4768 |
. 2
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4 | relco 4762 |
. . 3
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5 | dfrel3 4721 |
. . 3
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6 | 4, 5 | mpbi 133 |
. 2
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7 | 2, 3, 6 | 3eqtr2i 2063 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
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-14 1402 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 ax-sep 3866 ax-pow 3918 ax-pr 3935 |
This theorem depends on definitions: df-bi 110 df-3an 886 df-tru 1245 df-nf 1347 df-sb 1643 df-eu 1900 df-mo 1901 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-ral 2305 df-rex 2306 df-v 2553 df-un 2916 df-in 2918 df-ss 2925 df-pw 3353 df-sn 3373 df-pr 3374 df-op 3376 df-br 3756 df-opab 3810 df-xp 4294 df-rel 4295 df-cnv 4296 df-co 4297 df-res 4300 |
This theorem is referenced by: dfdm2 4795 cofunex2g 5681 |
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