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Mirrors > Home > MPE Home > Th. List > mpt2eq12 | Structured version Visualization version Unicode version |
Description: An equality theorem for the maps to notation. (Contributed by Mario Carneiro, 16-Dec-2013.) |
Ref | Expression |
---|---|
mpt2eq12 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2622 | . . . . 5 | |
2 | 1 | rgenw 2924 | . . . 4 |
3 | 2 | jctr 565 | . . 3 |
4 | 3 | ralrimivw 2967 | . 2 |
5 | mpt2eq123 6714 | . 2 | |
6 | 4, 5 | sylan2 491 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wceq 1483 wral 2912 cmpt2 6652 |
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-ral 2917 df-oprab 6654 df-mpt2 6655 |
This theorem is referenced by: dffi3 8337 cantnfres 8574 xpsval 16232 homffval 16350 comfffval 16358 monpropd 16397 natfval 16606 plusffval 17247 grpsubfval 17464 grpsubpropd2 17521 lsmvalx 18054 oppglsm 18057 lsmpropd 18090 dvrfval 18684 scaffval 18881 psrmulr 19384 psrplusgpropd 19606 ipffval 19993 marrepfval 20366 marepvfval 20371 d1mat2pmat 20544 txval 21367 cnmptk1p 21488 cnmptk2 21489 xpstopnlem1 21612 pcofval 22810 rrxmval 23188 madjusmdetlem1 29893 pstmval 29938 qqhval2 30026 mendplusgfval 37755 mendmulrfval 37757 mendvscafval 37760 funcrngcsetc 41998 funcringcsetc 42035 lmod1zr 42282 |
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