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Mirrors > Home > MPE Home > Th. List > coeq1i | Structured version Visualization version Unicode version |
Description: Equality inference for composition of two classes. (Contributed by NM, 16-Nov-2000.) |
Ref | Expression |
---|---|
coeq1i.1 |
Ref | Expression |
---|---|
coeq1i |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | coeq1i.1 | . 2 | |
2 | coeq1 5279 | . 2 | |
3 | 1, 2 | ax-mp 5 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wceq 1483 ccom 5118 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-in 3581 df-ss 3588 df-br 4654 df-opab 4713 df-co 5123 |
This theorem is referenced by: coeq12i 5285 cocnvcnv1 5646 hashgval 13120 imasdsval2 16176 prds1 18614 pf1mpf 19716 upxp 21426 uptx 21428 hoico2 28616 hoid1ri 28649 nmopcoadj2i 28961 pjclem3 29056 erdsze2lem2 31186 pprodcnveq 31990 diblss 36459 cononrel2 37901 trclubgNEW 37925 cortrcltrcl 38032 corclrtrcl 38033 cortrclrcl 38035 cotrclrtrcl 38036 cortrclrtrcl 38037 neicvgbex 38410 neicvgnvo 38413 dvsinax 40127 |
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