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Mirrors > Home > MPE Home > Th. List > rexrn | Structured version Visualization version Unicode version |
Description: Restricted existential quantification over the range of a function. (Contributed by Mario Carneiro, 24-Dec-2013.) (Revised by Mario Carneiro, 20-Aug-2014.) |
Ref | Expression |
---|---|
rexrn.1 |
Ref | Expression |
---|---|
rexrn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fvexd 6203 | . 2 | |
2 | fvelrnb 6243 | . . 3 | |
3 | eqcom 2629 | . . . 4 | |
4 | 3 | rexbii 3041 | . . 3 |
5 | 2, 4 | syl6bb 276 | . 2 |
6 | rexrn.1 | . . 3 | |
7 | 6 | adantl 482 | . 2 |
8 | 1, 5, 7 | rexxfr2d 4883 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wceq 1483 wcel 1990 wrex 2913 cvv 3200 crn 5115 wfn 5883 cfv 5888 |
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-iota 5851 df-fun 5890 df-fn 5891 df-fv 5896 |
This theorem is referenced by: elrnrexdm 6363 wemapwe 8594 rexanuz 14085 climsup 14400 supcvg 14588 ruclem12 14970 prmreclem6 15625 vdwmc 15682 znunit 19912 lmbr2 21063 lmff 21105 1stcfb 21248 imasf1oxms 22294 lebnumlem3 22762 lmmbr2 23057 lmcau 23111 bcthlem4 23124 mbfsup 23431 itg2monolem1 23517 itg2gt0 23527 ostth 25328 uhgrvtxedgiedgb 26031 dfnbgr3 26236 vdn0conngrumgrv2 27056 erdszelem10 31182 neibastop2lem 32355 filnetlem4 32376 mblfinlem2 33447 istotbnd3 33570 sstotbnd 33574 heibor 33620 nacsfix 37275 fnwe2lem2 37621 climinf 39838 |
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