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Mirrors > Home > ILE Home > Th. List > mpan10 | Unicode version |
Description: Modus ponens mixed with several conjunctions. (Contributed by Jim Kingdon, 7-Jan-2018.) |
Ref | Expression |
---|---|
mpan10 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ancom 264 |
. . . 4
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2 | 1 | anbi2i 448 |
. . 3
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3 | anass 396 |
. . 3
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4 | anass 396 |
. . 3
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5 | 2, 3, 4 | 3bitr4i 211 |
. 2
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6 | id 19 |
. . . 4
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7 | 6 | imp 123 |
. . 3
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8 | 7 | anim1i 336 |
. 2
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9 | 5, 8 | sylbi 120 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: (None) |
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