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Mirrors > Home > ILE Home > Th. List > imaundi | Unicode version |
Description: Distributive law for image over union. Theorem 35 of [Suppes] p. 65. (Contributed by NM, 30-Sep-2002.) |
Ref | Expression |
---|---|
imaundi |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | resundi 4920 |
. . . 4
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2 | 1 | rneqi 4855 |
. . 3
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3 | rnun 5037 |
. . 3
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4 | 2, 3 | eqtri 2198 |
. 2
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5 | df-ima 4639 |
. 2
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6 | df-ima 4639 |
. . 3
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7 | df-ima 4639 |
. . 3
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8 | 6, 7 | uneq12i 3287 |
. 2
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9 | 4, 5, 8 | 3eqtr4i 2208 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-v 2739 df-un 3133 df-in 3135 df-ss 3142 df-sn 3598 df-pr 3599 df-op 3601 df-br 4004 df-opab 4065 df-xp 4632 df-cnv 4634 df-dm 4636 df-rn 4637 df-res 4638 df-ima 4639 |
This theorem is referenced by: fnimapr 5576 fiintim 6927 fidcenumlemrks 6951 fidcenumlemr 6953 resunimafz0 10806 ennnfonelemhf1o 12408 |
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