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Mirrors > Home > MPE Home > Th. List > elima | Structured version Visualization version Unicode version |
Description: Membership in an image. Theorem 34 of [Suppes] p. 65. (Contributed by NM, 19-Apr-2004.) |
Ref | Expression |
---|---|
elima.1 |
Ref | Expression |
---|---|
elima |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elima.1 | . 2 | |
2 | elimag 5470 | . 2 | |
3 | 1, 2 | ax-mp 5 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wcel 1990 wrex 2913 cvv 3200 class class class wbr 4653 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-ral 2917 df-rex 2918 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: elima2 5472 rninxp 5573 imaco 5640 isarep1 5977 eliman0 6223 funimass4 6247 isomin 6587 dfsup2 8350 dfac10b 8961 hausmapdom 21303 pi1blem 22839 adjbd1o 28944 elintfv 31662 imaindm 31682 scutun12 31917 madeval2 31936 brimage 32033 dfrecs2 32057 dfrdg4 32058 dfint3 32059 imagesset 32060 elimaint 37940 elintima 37945 |
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