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Mirrors > Home > ILE Home > Th. List > iota1 | Unicode version |
Description: Property of iota. (Contributed by NM, 23-Aug-2011.) (Revised by Mario Carneiro, 23-Dec-2016.) |
Ref | Expression |
---|---|
iota1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-eu 2029 |
. 2
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2 | sp 1511 |
. . . . 5
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3 | iotaval 5189 |
. . . . . 6
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4 | 3 | eqeq2d 2189 |
. . . . 5
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5 | 2, 4 | bitr4d 191 |
. . . 4
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6 | eqcom 2179 |
. . . 4
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7 | 5, 6 | bitrdi 196 |
. . 3
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8 | 7 | exlimiv 1598 |
. 2
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9 | 1, 8 | sylbi 121 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-eu 2029 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-rex 2461 df-v 2739 df-sbc 2963 df-un 3133 df-sn 3598 df-pr 3599 df-uni 3810 df-iota 5178 |
This theorem is referenced by: iota2df 5202 sniota 5207 tz6.12-1 5542 riota1 5848 riota1a 5849 erovlem 6626 |
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