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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 6756 |
. . 3
| |
| 2 | elmapg 6748 |
. . 3
| |
| 3 | 1, 2 | syl 14 |
. 2
|
| 4 | 3 | ibi 176 |
1
|
| 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-in1 615 ax-in2 616 ax-io 711 ax-5 1470 ax-7 1471 ax-gen 1472 ax-ie1 1516 ax-ie2 1517 ax-8 1527 ax-10 1528 ax-11 1529 ax-i12 1530 ax-bndl 1532 ax-4 1533 ax-17 1549 ax-i9 1553 ax-ial 1557 ax-i5r 1558 ax-13 2178 ax-14 2179 ax-ext 2187 ax-sep 4162 ax-pow 4218 ax-pr 4253 ax-un 4480 ax-setind 4585 |
| This theorem depends on definitions: df-bi 117 df-3an 983 df-tru 1376 df-fal 1379 df-nf 1484 df-sb 1786 df-eu 2057 df-mo 2058 df-clab 2192 df-cleq 2198 df-clel 2201 df-nfc 2337 df-ne 2377 df-ral 2489 df-rex 2490 df-v 2774 df-sbc 2999 df-dif 3168 df-un 3170 df-in 3172 df-ss 3179 df-pw 3618 df-sn 3639 df-pr 3640 df-op 3642 df-uni 3851 df-br 4045 df-opab 4106 df-id 4340 df-xp 4681 df-rel 4682 df-cnv 4683 df-co 4684 df-dm 4685 df-rn 4686 df-iota 5232 df-fun 5273 df-fn 5274 df-f 5275 df-fv 5279 df-ov 5947 df-oprab 5948 df-mpo 5949 df-map 6737 |
| This theorem is referenced by: elmapfn 6758 elmapfun 6759 elmapssres 6760 mapsspm 6769 map0b 6774 mapss 6778 mapsncnv 6782 mapen 6943 mapxpen 6945 nninff 7224 ismkvnex 7257 nninfwlpoim 7281 nninfinfwlpo 7282 finacn 7316 acnccim 7384 psrbagf 14432 psrbagfi 14435 mplsubgfilemcl 14461 plycn 15234 dvply2g 15238 bj-charfunr 15746 2omap 15932 nninfalllem1 15945 nninfall 15946 nninfsellemdc 15947 nninfsellemqall 15952 nninfomnilem 15955 isomninnlem 15969 trilpo 15982 iswomninnlem 15988 iswomni0 15990 ismkvnnlem 15991 redcwlpo 15994 nconstwlpo 16005 neapmkv 16007 |
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