Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rn 4620 | . . . 4 | |
2 | frn 5354 | . . . . 5 | |
3 | 2 | adantr 274 | . . . 4 |
4 | 1, 3 | eqsstrrid 3194 | . . 3 |
5 | ssdisj 3470 | . . 3 | |
6 | 4, 5 | sylancom 418 | . 2 |
7 | imadisj 4971 | . 2 | |
8 | 6, 7 | sylibr 133 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1348 cin 3120 wss 3121 c0 3414 ccnv 4608 cdm 4609 crn 4610 cima 4612 wf 5192 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 609 ax-in2 610 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-14 2144 ax-ext 2152 ax-sep 4105 ax-pow 4158 ax-pr 4192 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-fal 1354 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-dif 3123 df-un 3125 df-in 3127 df-ss 3134 df-nul 3415 df-pw 3566 df-sn 3587 df-pr 3588 df-op 3590 df-br 3988 df-opab 4049 df-xp 4615 df-cnv 4617 df-dm 4619 df-rn 4620 df-res 4621 df-ima 4622 df-f 5200 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |