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Mirrors > Home > MPE Home > Th. List > coeq2i | 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 |
---|---|
coeq2i |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | coeq1i.1 | . 2 | |
2 | coeq2 5280 | . 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 cocnvcnv2 5647 co01 5650 fcoi1 6078 dftpos2 7369 tposco 7383 canthp1 9476 cats1co 13601 isoval 16425 mvdco 17865 evlsval 19519 evl1fval1lem 19694 evl1var 19700 pf1ind 19719 imasdsf1olem 22178 hoico1 28615 hoid1i 28648 pjclem1 29054 pjclem3 29056 pjci 29059 dfpo2 31645 poimirlem9 33418 cdlemk45 36235 cononrel1 37900 trclubgNEW 37925 trclrelexplem 38003 relexpaddss 38010 cotrcltrcl 38017 cortrcltrcl 38032 corclrtrcl 38033 cotrclrcl 38034 cortrclrcl 38035 cotrclrtrcl 38036 cortrclrtrcl 38037 brco3f1o 38331 clsneibex 38400 neicvgbex 38410 subsaliuncl 40576 meadjiun 40683 |
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