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Mirrors > Home > MPE Home > Th. List > coeq12i | Structured version Visualization version Unicode version |
Description: Equality inference for composition of two classes. (Contributed by FL, 7-Jun-2012.) |
Ref | Expression |
---|---|
coeq12i.1 | |
coeq12i.2 |
Ref | Expression |
---|---|
coeq12i |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | coeq12i.1 | . . 3 | |
2 | 1 | coeq1i 5281 | . 2 |
3 | coeq12i.2 | . . 3 | |
4 | 3 | coeq2i 5282 | . 2 |
5 | 2, 4 | eqtri 2644 | 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: madetsumid 20267 mdetleib2 20394 imsval 27540 pjcmul1i 29060 cotrcltrcl 38017 brtrclfv2 38019 clsneif1o 38402 |
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