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Mirrors > Home > MPE Home > Th. List > elimasn | Structured version Visualization version Unicode version |
Description: Membership in an image of a singleton. (Contributed by NM, 15-Mar-2004.) (Proof shortened by Andrew Salmon, 27-Aug-2011.) |
Ref | Expression |
---|---|
elimasn.1 | |
elimasn.2 |
Ref | Expression |
---|---|
elimasn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elimasn.2 | . . 3 | |
2 | breq2 4657 | . . 3 | |
3 | elimasn.1 | . . . 4 | |
4 | imasng 5487 | . . . 4 | |
5 | 3, 4 | ax-mp 5 | . . 3 |
6 | 1, 2, 5 | elab2 3354 | . 2 |
7 | df-br 4654 | . 2 | |
8 | 6, 7 | bitri 264 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wceq 1483 wcel 1990 cab 2608 cvv 3200 csn 4177 cop 4183 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-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-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: elimasng 5491 dfco2 5634 dfco2a 5635 ressn 5671 funfvima3 6495 frxp 7287 marypha1lem 8339 gsum2dlem1 18369 gsum2dlem2 18370 gsum2d 18371 gsum2d2 18373 ovoliunlem1 23270 iunsnima 29428 dfcnv2 29476 gsummpt2co 29780 gsummpt2d 29781 dmscut 31918 scutf 31919 funpartfun 32050 areaquad 37802 dffrege76 38233 frege97 38254 frege98 38255 frege109 38266 frege110 38267 frege131 38288 frege133 38290 |
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