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Mirrors > Home > MPE Home > Th. List > spimt | Structured version Visualization version Unicode version |
Description: Closed theorem form of spim 2098. (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 | ax6e 2094 |
. . . 4
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2 | exim 1706 |
. . . 4
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3 | 1, 2 | mpi 20 |
. . 3
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4 | 19.35 1740 |
. . 3
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5 | 3, 4 | sylib 200 |
. 2
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6 | 19.9t 1969 |
. . 3
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7 | 6 | biimpd 211 |
. 2
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8 | 5, 7 | sylan9r 664 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-10 1915 ax-12 1933 ax-13 2091 |
This theorem depends on definitions: df-bi 189 df-an 373 df-ex 1664 df-nf 1668 |
This theorem is referenced by: (None) |
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