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Mirrors > Home > MPE Home > Th. List > iota4 | Structured version Visualization version Unicode version |
Description: Theorem *14.22 in [WhiteheadRussell] p. 190. (Contributed by Andrew Salmon, 12-Jul-2011.) |
Ref | Expression |
---|---|
iota4 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-eu 2313 |
. 2
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2 | biimpr 203 |
. . . . . 6
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3 | 2 | alimi 1694 |
. . . . 5
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4 | sb2 2193 |
. . . . 5
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5 | 3, 4 | syl 17 |
. . . 4
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6 | iotaval 5575 |
. . . . . 6
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7 | 6 | eqcomd 2467 |
. . . . 5
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8 | dfsbcq2 3281 |
. . . . 5
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9 | 7, 8 | syl 17 |
. . . 4
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10 | 5, 9 | mpbid 215 |
. . 3
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11 | 10 | exlimiv 1786 |
. 2
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12 | 1, 11 | sylbi 200 |
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 1679 ax-4 1692 ax-5 1768 ax-6 1815 ax-7 1861 ax-10 1925 ax-11 1930 ax-12 1943 ax-13 2101 ax-ext 2441 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-tru 1457 df-ex 1674 df-nf 1678 df-sb 1808 df-eu 2313 df-clab 2448 df-cleq 2454 df-clel 2457 df-nfc 2591 df-rex 2754 df-v 3058 df-sbc 3279 df-un 3420 df-sn 3980 df-pr 3982 df-uni 4212 df-iota 5564 |
This theorem is referenced by: iota4an 5583 iotacl 5587 pm14.24 36826 sbiota1 36828 |
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