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Mirrors > Home > NFE 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 2208 |
. 2
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2 | sp 1747 |
. . . . 5
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3 | iotaval 4350 |
. . . . . 6
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4 | 3 | eqeq2d 2364 |
. . . . 5
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5 | 2, 4 | bitr4d 247 |
. . . 4
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6 | eqcom 2355 |
. . . 4
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7 | 5, 6 | syl6bb 252 |
. . 3
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8 | 7 | exlimiv 1634 |
. 2
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9 | 1, 8 | sylbi 187 |
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 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-eu 2208 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-rex 2620 df-v 2861 df-sbc 3047 df-nin 3211 df-compl 3212 df-un 3214 df-sn 3741 df-pr 3742 df-uni 3892 df-iota 4339 |
This theorem is referenced by: iota2df 4365 sniota 4369 |
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