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Mirrors > Home > ILE Home > Th. List > coeq1 | Unicode version |
Description: Equality theorem for composition of two classes. (Contributed by NM, 3-Jan-1997.) |
Ref | Expression |
---|---|
coeq1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | coss1 4764 | . . 3 | |
2 | coss1 4764 | . . 3 | |
3 | 1, 2 | anim12i 336 | . 2 |
4 | eqss 3162 | . 2 | |
5 | eqss 3162 | . 2 | |
6 | 3, 4, 5 | 3imtr4i 200 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1348 wss 3121 ccom 4613 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-in 3127 df-ss 3134 df-br 3988 df-opab 4049 df-co 4618 |
This theorem is referenced by: coeq1i 4768 coeq1d 4770 coi2 5125 relcnvtr 5128 funcoeqres 5471 ereq1 6516 updjud 7055 |
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