![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > imaundi | Structured version Visualization version Unicode version |
Description: Distributive law for image over union. Theorem 35 of [Suppes] p. 65. (Contributed by NM, 30-Sep-2002.) |
Ref | Expression |
---|---|
imaundi |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | resundi 5118 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | 1 | rneqi 5061 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
3 | rnun 5244 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | 2, 3 | eqtri 2473 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
5 | df-ima 4847 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
6 | df-ima 4847 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
7 | df-ima 4847 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
8 | 6, 7 | uneq12i 3586 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
9 | 4, 5, 8 | 3eqtr4i 2483 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-10 1915 ax-11 1920 ax-12 1933 ax-13 2091 ax-ext 2431 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3an 987 df-tru 1447 df-ex 1664 df-nf 1668 df-sb 1798 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2581 df-rab 2746 df-v 3047 df-dif 3407 df-un 3409 df-in 3411 df-ss 3418 df-nul 3732 df-if 3882 df-sn 3969 df-pr 3971 df-op 3975 df-br 4403 df-opab 4462 df-xp 4840 df-cnv 4842 df-dm 4844 df-rn 4845 df-res 4846 df-ima 4847 |
This theorem is referenced by: fnimapr 5929 domunfican 7844 fiint 7848 fodomfi 7850 marypha1lem 7947 dprd2da 17675 dmdprdsplit2lem 17678 uniioombllem3 22543 mbfimaicc 22589 plyeq0 23165 eupath2lem3 25707 ffsrn 28314 imadifss 31928 poimirlem1 31941 poimirlem2 31942 poimirlem3 31943 poimirlem4 31944 poimirlem6 31946 poimirlem7 31947 poimirlem11 31951 poimirlem12 31952 poimirlem15 31955 poimirlem16 31956 poimirlem17 31957 poimirlem19 31959 poimirlem20 31960 poimirlem23 31963 poimirlem24 31964 poimirlem25 31965 poimirlem29 31969 poimirlem31 31971 mbfposadd 31988 itg2addnclem2 31994 ftc1anclem1 32017 ftc1anclem5 32021 brtrclfv2 36319 frege77d 36338 frege109d 36349 frege131d 36356 dffrege76 36535 icccncfext 37765 |
Copyright terms: Public domain | W3C validator |