Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 2000 | . 2 | |
2 | bi2 129 | . . . . . 6 | |
3 | 2 | alimi 1431 | . . . . 5 |
4 | sb2 1740 | . . . . 5 | |
5 | 3, 4 | syl 14 | . . . 4 |
6 | iotaval 5094 | . . . . . 6 | |
7 | 6 | eqcomd 2143 | . . . . 5 |
8 | dfsbcq2 2907 | . . . . 5 | |
9 | 7, 8 | syl 14 | . . . 4 |
10 | 5, 9 | mpbid 146 | . . 3 |
11 | 10 | exlimiv 1577 | . 2 |
12 | 1, 11 | sylbi 120 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wal 1329 wceq 1331 wex 1468 wsb 1735 weu 1997 wsbc 2904 cio 5081 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2000 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-rex 2420 df-v 2683 df-sbc 2905 df-un 3070 df-sn 3528 df-pr 3529 df-uni 3732 df-iota 5083 |
This theorem is referenced by: iota4an 5102 iotacl 5106 |
Copyright terms: Public domain | W3C validator |