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Mirrors > Home > ILE Home > Th. List > spimt | Unicode version |
Description: Closed theorem form of spim 1716. (Contributed by NM, 15-Jan-2008.) (Revised by Mario Carneiro, 17-Oct-2016.) (Proof shortened by Wolf Lammen, 24-Feb-2018.) |
Ref | Expression |
---|---|
spimt |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | a9e 1674 | . . . 4 | |
2 | exim 1578 | . . . 4 | |
3 | 1, 2 | mpi 15 | . . 3 |
4 | 19.35-1 1603 | . . 3 | |
5 | 3, 4 | syl 14 | . 2 |
6 | 19.9t 1621 | . . 3 | |
7 | 6 | biimpd 143 | . 2 |
8 | 5, 7 | sylan9r 407 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wal 1329 wceq 1331 wnf 1436 wex 1468 |
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-5 1423 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-4 1487 ax-i9 1510 ax-ial 1514 |
This theorem depends on definitions: df-bi 116 df-nf 1437 |
This theorem is referenced by: spimd 12961 |
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