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Mirrors > Home > MPE Home > Th. List > mptv | Structured version Unicode version |
Description: Function with universal domain in maps-to notation. (Contributed by NM, 16-Aug-2013.) |
Ref | Expression |
---|---|
mptv |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-mpt 4461 |
. 2
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2 | vex 3081 |
. . . 4
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3 | 2 | biantrur 506 |
. . 3
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4 | 3 | opabbii 4465 |
. 2
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5 | 1, 4 | eqtr4i 2486 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1955 ax-ext 2432 |
This theorem depends on definitions: df-bi 185 df-an 371 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-clab 2440 df-cleq 2446 df-clel 2449 df-v 3080 df-opab 4460 df-mpt 4461 |
This theorem is referenced by: df1st2 6770 df2nd2 6771 fsplit 6788 rankf 8113 cnmptid 19367 |
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