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Mirrors > Home > ILE Home > Th. List > mpofvexi | Unicode version |
Description: Sufficient condition for an operation maps-to notation to be set-like. (Contributed by Mario Carneiro, 3-Jul-2019.) |
Ref | Expression |
---|---|
fmpo.1 | |
fnmpoi.2 | |
mpofvexi.3 | |
mpofvexi.4 |
Ref | Expression |
---|---|
mpofvexi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fnmpoi.2 | . . 3 | |
2 | 1 | gen2 1430 | . 2 |
3 | mpofvexi.3 | . 2 | |
4 | mpofvexi.4 | . 2 | |
5 | fmpo.1 | . . 3 | |
6 | 5 | mpofvex 6152 | . 2 |
7 | 2, 3, 4, 6 | mp3an 1319 | 1 |
Colors of variables: wff set class |
Syntax hints: wal 1333 wceq 1335 wcel 2128 cvv 2712 (class class class)co 5825 cmpo 5827 |
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-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-13 2130 ax-14 2131 ax-ext 2139 ax-sep 4083 ax-pow 4136 ax-pr 4170 ax-un 4394 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-sbc 2938 df-csb 3032 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-uni 3774 df-iun 3852 df-br 3967 df-opab 4027 df-mpt 4028 df-id 4254 df-xp 4593 df-rel 4594 df-cnv 4595 df-co 4596 df-dm 4597 df-rn 4598 df-iota 5136 df-fun 5173 df-fn 5174 df-f 5175 df-fo 5177 df-fv 5179 df-ov 5828 df-oprab 5829 df-mpo 5830 df-1st 6089 df-2nd 6090 |
This theorem is referenced by: (None) |
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