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Mirrors > Home > ILE Home > Th. List > coeq2 | Unicode version |
Description: Equality theorem for composition of two classes. (Contributed by NM, 3-Jan-1997.) |
Ref | Expression |
---|---|
coeq2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | coss2 4435 |
. . 3
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2 | coss2 4435 |
. . 3
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3 | 1, 2 | anim12i 321 |
. 2
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4 | eqss 2954 |
. 2
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5 | eqss 2954 |
. 2
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6 | 3, 4, 5 | 3imtr4i 190 |
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-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-co 4297 |
This theorem is referenced by: coeq2i 4439 coeq2d 4441 coi2 4780 relcnvtr 4783 relcoi1 4792 f1eqcocnv 5374 ereq1 6049 |
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