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Mirrors > Home > ILE Home > Th. List > pm5.74 | Unicode version |
Description: Distribution of implication over biconditional. Theorem *5.74 of [WhiteheadRussell] p. 126. (Contributed by NM, 1-Aug-1994.) (Proof shortened by Wolf Lammen, 11-Apr-2013.) |
Ref | Expression |
---|---|
pm5.74 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bi1 116 |
. . . 4
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2 | 1 | imim3i 60 |
. . 3
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3 | bi2 128 |
. . . 4
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4 | 3 | imim3i 60 |
. . 3
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5 | 2, 4 | impbid 127 |
. 2
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6 | bi1 116 |
. . . 4
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7 | 6 | pm2.86d 98 |
. . 3
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8 | bi2 128 |
. . . 4
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9 | 8 | pm2.86d 98 |
. . 3
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10 | 7, 9 | impbidd 125 |
. 2
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11 | 5, 10 | impbii 124 |
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 104 ax-ia2 105 ax-ia3 106 |
This theorem depends on definitions: df-bi 115 |
This theorem is referenced by: pm5.74i 178 pm5.74ri 179 pm5.74d 180 pm5.74rd 181 bibi2d 230 |
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