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Mirrors > Home > ILE Home > Th. List > elmapi | Unicode version |
Description: A mapping is a function, forward direction only with superfluous antecedent removed. (Contributed by Stefan O'Rear, 10-Oct-2014.) |
Ref | Expression |
---|---|
elmapi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elmapex 6647 | . . 3 | |
2 | elmapg 6639 | . . 3 | |
3 | 1, 2 | syl 14 | . 2 |
4 | 3 | ibi 175 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wcel 2141 cvv 2730 wf 5194 (class class class)co 5853 cmap 6626 |
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-13 2143 ax-14 2144 ax-ext 2152 ax-sep 4107 ax-pow 4160 ax-pr 4194 ax-un 4418 ax-setind 4521 |
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-ne 2341 df-ral 2453 df-rex 2454 df-v 2732 df-sbc 2956 df-dif 3123 df-un 3125 df-in 3127 df-ss 3134 df-pw 3568 df-sn 3589 df-pr 3590 df-op 3592 df-uni 3797 df-br 3990 df-opab 4051 df-id 4278 df-xp 4617 df-rel 4618 df-cnv 4619 df-co 4620 df-dm 4621 df-rn 4622 df-iota 5160 df-fun 5200 df-fn 5201 df-f 5202 df-fv 5206 df-ov 5856 df-oprab 5857 df-mpo 5858 df-map 6628 |
This theorem is referenced by: elmapfn 6649 elmapfun 6650 elmapssres 6651 mapsspm 6660 map0b 6665 mapss 6669 mapsncnv 6673 mapen 6824 mapxpen 6826 nninff 7099 ismkvnex 7131 nninfwlpoim 7154 bj-charfunr 13845 nninfalllem1 14041 nninfall 14042 nninfsellemdc 14043 nninfsellemqall 14048 nninfomnilem 14051 isomninnlem 14062 trilpo 14075 iswomninnlem 14081 iswomni0 14083 ismkvnnlem 14084 redcwlpo 14087 nconstwlpo 14097 neapmkv 14099 |
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