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Mirrors > Home > ILE Home > Th. List > iota4 | Unicode version |
Description: Theorem *14.22 in [WhiteheadRussell] p. 190. (Contributed by Andrew Salmon, 12-Jul-2011.) |
Ref | Expression |
---|---|
iota4 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-eu 2022 | . 2 | |
2 | biimpr 129 | . . . . . 6 | |
3 | 2 | alimi 1448 | . . . . 5 |
4 | sb2 1760 | . . . . 5 | |
5 | 3, 4 | syl 14 | . . . 4 |
6 | iotaval 5169 | . . . . . 6 | |
7 | 6 | eqcomd 2176 | . . . . 5 |
8 | dfsbcq2 2958 | . . . . 5 | |
9 | 7, 8 | syl 14 | . . . 4 |
10 | 5, 9 | mpbid 146 | . . 3 |
11 | 10 | exlimiv 1591 | . 2 |
12 | 1, 11 | sylbi 120 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wal 1346 wceq 1348 wex 1485 wsb 1755 weu 2019 wsbc 2955 cio 5156 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-rex 2454 df-v 2732 df-sbc 2956 df-un 3125 df-sn 3587 df-pr 3588 df-uni 3795 df-iota 5158 |
This theorem is referenced by: iota4an 5177 iotacl 5181 |
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