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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 4828 |
. 2
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2 | euiotaex 4826 |
. . . 4
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3 | simpl 102 |
. . . . 5
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4 | 3 | sbcth 2771 |
. . . 4
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5 | 2, 4 | syl 14 |
. . 3
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6 | sbcimg 2798 |
. . . 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 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-tru 1245 df-nf 1347 df-sb 1643 df-eu 1900 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-rex 2306 df-v 2553 df-sbc 2759 df-un 2916 df-sn 3373 df-pr 3374 df-uni 3572 df-iota 4810 |
This theorem is referenced by: (None) |
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