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Mirrors > Home > ILE Home > Th. List > spimt | Unicode version |
Description: Closed theorem form of spim 1717. (Contributed by NM, 15-Jan-2008.) (Revised by Mario Carneiro, 17-Oct-2016.) (Proof shortened by Wolf Lammen, 24-Feb-2018.) |
Ref | Expression |
---|---|
spimt |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | a9e 1675 |
. . . 4
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2 | exim 1579 |
. . . 4
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3 | 1, 2 | mpi 15 |
. . 3
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4 | 19.35-1 1604 |
. . 3
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5 | 3, 4 | syl 14 |
. 2
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6 | 19.9t 1622 |
. . 3
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7 | 6 | biimpd 143 |
. 2
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8 | 5, 7 | sylan9r 408 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
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 1424 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-4 1488 ax-i9 1511 ax-ial 1515 |
This theorem depends on definitions: df-bi 116 df-nf 1438 |
This theorem is referenced by: spimd 13143 |
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