Mathbox for Alexander van der Vekens |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > dfaimafn2 | Structured version Visualization version Unicode version |
Description: Alternate definition of the image of a function as an indexed union of singletons of function values, analogous to dfimafn2 6246. (Contributed by Alexander van der Vekens, 25-May-2017.) |
Ref | Expression |
---|---|
dfaimafn2 | ''' |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfaimafn 41245 | . . 3 ''' | |
2 | iunab 4566 | . . 3 ''' ''' | |
3 | 1, 2 | syl6eqr 2674 | . 2 ''' |
4 | df-sn 4178 | . . . . 5 ''' ''' | |
5 | eqcom 2629 | . . . . . 6 ''' ''' | |
6 | 5 | abbii 2739 | . . . . 5 ''' ''' |
7 | 4, 6 | eqtri 2644 | . . . 4 ''' ''' |
8 | 7 | a1i 11 | . . 3 ''' ''' |
9 | 8 | iuneq2i 4539 | . 2 ''' ''' |
10 | 3, 9 | syl6eqr 2674 | 1 ''' |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wceq 1483 wcel 1990 cab 2608 wrex 2913 wss 3574 csn 4177 ciun 4520 cdm 5114 cima 5117 wfun 5882 '''cafv 41194 |
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-iun 4522 df-br 4654 df-opab 4713 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-fv 5896 df-dfat 41196 df-afv 41197 |
This theorem is referenced by: (None) |
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