Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > i1frn | Structured version Visualization version Unicode version |
Description: A simple function has finite range. (Contributed by Mario Carneiro, 26-Jun-2014.) |
Ref | Expression |
---|---|
i1frn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | isi1f 23441 | . . 3 MblFn | |
2 | 1 | simprbi 480 | . 2 |
3 | 2 | simp2d 1074 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 w3a 1037 wcel 1990 cdif 3571 csn 4177 ccnv 5113 cdm 5114 crn 5115 cima 5117 wf 5884 cfv 5888 cfn 7955 cr 9935 cc0 9936 cvol 23232 MblFncmbf 23383 citg1 23384 |
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-rn 5125 df-res 5126 df-ima 5127 df-iota 5851 df-fun 5890 df-fn 5891 df-f 5892 df-fv 5896 df-sum 14417 df-itg1 23389 |
This theorem is referenced by: i1fima 23445 itg1cl 23452 itg1ge0 23453 i1fadd 23462 i1fmul 23463 itg1addlem4 23466 itg1addlem5 23467 i1fmulc 23470 itg1mulc 23471 i1fres 23472 itg10a 23477 itg1ge0a 23478 itg1climres 23481 itg2addnclem2 33462 ftc1anclem3 33487 ftc1anclem6 33490 ftc1anclem7 33491 ftc1anc 33493 |
Copyright terms: Public domain | W3C validator |