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Mirrors > Home > ILE Home > Th. List > iota4an | Unicode version |
Description: Theorem *14.23 in [WhiteheadRussell] p. 191. (Contributed by Andrew Salmon, 12-Jul-2011.) |
Ref | Expression |
---|---|
iota4an |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iota4 4885 |
. 2
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2 | euiotaex 4883 |
. . . 4
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3 | simpl 102 |
. . . . 5
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4 | 3 | sbcth 2777 |
. . . 4
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5 | 2, 4 | syl 14 |
. . 3
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6 | sbcimg 2804 |
. . . 4
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7 | 2, 6 | syl 14 |
. . 3
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8 | 5, 7 | mpbid 135 |
. 2
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9 | 1, 8 | mpd 13 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-eu 1903 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-rex 2312 df-v 2559 df-sbc 2765 df-un 2922 df-sn 3381 df-pr 3382 df-uni 3581 df-iota 4867 |
This theorem is referenced by: (None) |
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