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Mirrors > Home > MPE Home > Th. List > qnumval | Structured version Visualization version Unicode version |
Description: Value of the canonical numerator function. (Contributed by Stefan O'Rear, 13-Sep-2014.) |
Ref | Expression |
---|---|
qnumval | numer |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqeq1 2626 | . . . . 5 | |
2 | 1 | anbi2d 740 | . . . 4 |
3 | 2 | riotabidv 6613 | . . 3 |
4 | 3 | fveq2d 6195 | . 2 |
5 | df-numer 15443 | . 2 numer | |
6 | fvex 6201 | . 2 | |
7 | 4, 5, 6 | fvmpt 6282 | 1 numer |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wceq 1483 wcel 1990 cxp 5112 cfv 5888 crio 6610 (class class class)co 6650 c1st 7166 c2nd 7167 c1 9937 cdiv 10684 cn 11020 cz 11377 cq 11788 cgcd 15216 numercnumer 15441 |
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 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-mpt 4730 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-iota 5851 df-fun 5890 df-fv 5896 df-riota 6611 df-numer 15443 |
This theorem is referenced by: qnumdencl 15447 fnum 15450 qnumdenbi 15452 |
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