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Mirrors > Home > MPE Home > Th. List > mpteq12 | Structured version Visualization version Unicode version |
Description: An equality theorem for the maps to notation. (Contributed by NM, 16-Dec-2013.) |
Ref | Expression |
---|---|
mpteq12 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-5 1839 | . 2 | |
2 | mpteq12f 4731 | . 2 | |
3 | 1, 2 | sylan 488 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wal 1481 wceq 1483 wral 2912 cmpt 4729 |
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-ral 2917 df-opab 4713 df-mpt 4730 |
This theorem is referenced by: mpteq1 4737 mpteqb 6299 fmptcof 6397 mapxpen 8126 prodeq2w 14642 prdsdsval2 16144 prdsdsval3 16145 ablfac2 18488 mdetunilem9 20426 mdetmul 20429 xkocnv 21617 voliun 23322 itgeq1f 23538 itgeq2 23544 iblcnlem 23555 esumeq2 30098 esumcvg 30148 dvtan 33460 bddiblnc 33480 |
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