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Mirrors > Home > MPE Home > Th. List > riotaprop | Structured version Unicode version |
Description: Properties of a restricted definite description operator. Todo (df-riota 6164 update): can some uses of riota2f 6186 be shortened with this? (Contributed by NM, 23-Nov-2013.) |
Ref | Expression |
---|---|
riotaprop.0 |
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riotaprop.1 |
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riotaprop.2 |
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Ref | Expression |
---|---|
riotaprop |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | riotaprop.1 |
. . 3
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2 | riotacl 6179 |
. . 3
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3 | 1, 2 | syl5eqel 2546 |
. 2
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4 | 1 | eqcomi 2467 |
. . . 4
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5 | nfriota1 6171 |
. . . . . 6
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6 | 1, 5 | nfcxfr 2614 |
. . . . 5
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7 | riotaprop.0 |
. . . . 5
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8 | riotaprop.2 |
. . . . 5
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9 | 6, 7, 8 | riota2f 6186 |
. . . 4
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10 | 4, 9 | mpbiri 233 |
. . 3
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11 | 3, 10 | mpancom 669 |
. 2
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12 | 3, 11 | jca 532 |
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-3an 967 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-eu 2266 df-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2604 df-ral 2804 df-rex 2805 df-reu 2806 df-rab 2808 df-v 3080 df-sbc 3295 df-un 3444 df-in 3446 df-ss 3453 df-sn 3989 df-pr 3991 df-uni 4203 df-iota 5492 df-riota 6164 |
This theorem is referenced by: fin23lem27 8611 lble 10396 ltrniotaval 34583 |
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