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Mirrors > Home > ILE Home > Th. List > fimacnvdisj | Unicode version |
Description: The preimage of a class disjoint with a mapping's codomain is empty. (Contributed by FL, 24-Jan-2007.) |
Ref | Expression |
---|---|
fimacnvdisj |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rn 4402 |
. . . 4
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2 | frn 5103 |
. . . . 5
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3 | 2 | adantr 270 |
. . . 4
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4 | 1, 3 | syl5eqssr 3053 |
. . 3
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5 | ssdisj 3316 |
. . 3
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6 | 4, 5 | sylancom 411 |
. 2
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7 | imadisj 4737 |
. 2
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8 | 6, 7 | sylibr 132 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 577 ax-in2 578 ax-io 663 ax-5 1377 ax-7 1378 ax-gen 1379 ax-ie1 1423 ax-ie2 1424 ax-8 1436 ax-10 1437 ax-11 1438 ax-i12 1439 ax-bndl 1440 ax-4 1441 ax-14 1446 ax-17 1460 ax-i9 1464 ax-ial 1468 ax-i5r 1469 ax-ext 2065 ax-sep 3916 ax-pow 3968 ax-pr 3992 |
This theorem depends on definitions: df-bi 115 df-3an 922 df-tru 1288 df-fal 1291 df-nf 1391 df-sb 1688 df-eu 1946 df-mo 1947 df-clab 2070 df-cleq 2076 df-clel 2079 df-nfc 2212 df-ral 2358 df-rex 2359 df-v 2612 df-dif 2984 df-un 2986 df-in 2988 df-ss 2995 df-nul 3268 df-pw 3402 df-sn 3422 df-pr 3423 df-op 3425 df-br 3806 df-opab 3860 df-xp 4397 df-cnv 4399 df-dm 4401 df-rn 4402 df-res 4403 df-ima 4404 df-f 4956 |
This theorem is referenced by: (None) |
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