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Mirrors > Home > MPE Home > Th. List > mptun | Structured version Unicode version |
Description: Union of mappings which are mutually compatible. (Contributed by Mario Carneiro, 31-Aug-2015.) |
Ref | Expression |
---|---|
mptun |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-mpt 4463 |
. 2
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2 | df-mpt 4463 |
. . . 4
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3 | df-mpt 4463 |
. . . 4
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4 | 2, 3 | uneq12i 3619 |
. . 3
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5 | elun 3608 |
. . . . . . 7
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6 | 5 | anbi1i 695 |
. . . . . 6
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7 | andir 863 |
. . . . . 6
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8 | 6, 7 | bitri 249 |
. . . . 5
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9 | 8 | opabbii 4467 |
. . . 4
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10 | unopab 4478 |
. . . 4
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11 | 9, 10 | eqtr4i 2486 |
. . 3
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12 | 4, 11 | eqtr4i 2486 |
. 2
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13 | 1, 12 | 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-or 370 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-nfc 2604 df-v 3080 df-un 3444 df-opab 4462 df-mpt 4463 |
This theorem is referenced by: fmptap 6013 fmptapd 6014 partfun 26171 ptrest 28596 |
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