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Mirrors > Home > MPE Home > Th. List > ima0 | Structured version Visualization version Unicode version |
Description: Image of the empty set. Theorem 3.16(ii) of [Monk1] p. 38. (Contributed by NM, 20-May-1998.) |
Ref | Expression |
---|---|
ima0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ima 5127 | . 2 | |
2 | res0 5400 | . . 3 | |
3 | 2 | rneqi 5352 | . 2 |
4 | rn0 5377 | . 2 | |
5 | 1, 3, 4 | 3eqtri 2648 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wceq 1483 c0 3915 crn 5115 cres 5116 cima 5117 |
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-rab 2921 df-v 3202 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-br 4654 df-opab 4713 df-xp 5120 df-cnv 5122 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 |
This theorem is referenced by: csbima12 5483 relimasn 5488 elimasni 5492 inisegn0 5497 dffv3 6187 supp0cosupp0 7334 imacosupp 7335 ecexr 7747 domunfican 8233 fodomfi 8239 efgrelexlema 18162 dprdsn 18435 cnindis 21096 cnhaus 21158 cmpfi 21211 xkouni 21402 xkoccn 21422 mbfima 23399 ismbf2d 23408 limcnlp 23642 mdeg0 23830 pserulm 24176 spthispth 26622 pthdlem2 26664 0pth 26986 1pthdlem2 26996 eupth2lemb 27097 disjpreima 29397 imadifxp 29414 dstrvprob 30533 opelco3 31678 funpartlem 32049 poimirlem1 33410 poimirlem2 33411 poimirlem3 33412 poimirlem4 33413 poimirlem5 33414 poimirlem6 33415 poimirlem7 33416 poimirlem10 33419 poimirlem11 33420 poimirlem12 33421 poimirlem13 33422 poimirlem16 33425 poimirlem17 33426 poimirlem19 33428 poimirlem20 33429 poimirlem22 33431 poimirlem23 33432 poimirlem24 33433 poimirlem25 33434 poimirlem28 33437 poimirlem29 33438 poimirlem31 33440 he0 38078 smfresal 40995 |
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