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Mirrors > Home > ILE Home > Th. List > coeq12d | Unicode version |
Description: Equality deduction for composition of two classes. (Contributed by FL, 7-Jun-2012.) |
Ref | Expression |
---|---|
coeq12d.1 | |
coeq12d.2 |
Ref | Expression |
---|---|
coeq12d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | coeq12d.1 | . . 3 | |
2 | 1 | coeq1d 4695 | . 2 |
3 | coeq12d.2 | . . 3 | |
4 | 3 | coeq2d 4696 | . 2 |
5 | 2, 4 | eqtrd 2170 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1331 ccom 4538 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-in 3072 df-ss 3079 df-br 3925 df-opab 3985 df-co 4543 |
This theorem is referenced by: (None) |
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