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Mirrors > Home > ILE Home > Th. List > mptv | Unicode version |
Description: Function with universal domain in maps-to notation. (Contributed by NM, 16-Aug-2013.) |
Ref | Expression |
---|---|
mptv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-mpt 4027 | . 2 | |
2 | vex 2715 | . . . 4 | |
3 | 2 | biantrur 301 | . . 3 |
4 | 3 | opabbii 4031 | . 2 |
5 | 1, 4 | eqtr4i 2181 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1335 wcel 2128 cvv 2712 copab 4024 cmpt 4025 |
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-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-11 1486 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-v 2714 df-opab 4026 df-mpt 4027 |
This theorem is referenced by: df1st2 6163 df2nd2 6164 hashennn 10649 cnmptid 12668 |
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