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Mirrors > Home > ILE Home > Th. List > pm5.75 | Unicode version |
Description: Theorem *5.75 of [WhiteheadRussell] p. 126. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Andrew Salmon, 7-May-2011.) (Proof shortened by Wolf Lammen, 23-Dec-2012.) |
Ref | Expression |
---|---|
pm5.75 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | anbi1 466 |
. . 3
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2 | orcom 728 |
. . . . 5
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3 | 2 | anbi1i 458 |
. . . 4
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4 | pm5.61 794 |
. . . 4
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5 | 3, 4 | bitri 184 |
. . 3
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6 | 1, 5 | bitrdi 196 |
. 2
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7 | pm4.71 389 |
. . . 4
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8 | 7 | biimpi 120 |
. . 3
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9 | 8 | bicomd 141 |
. 2
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10 | 6, 9 | sylan9bbr 463 |
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 106 ax-ia2 107 ax-ia3 108 ax-in2 615 ax-io 709 |
This theorem depends on definitions: df-bi 117 |
This theorem is referenced by: (None) |
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