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Mirrors > Home > NFE 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 178 |
. . . 4
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2 | 1 | imim3i 55 |
. . 3
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3 | bi2 189 |
. . . 4
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4 | 3 | imim3i 55 |
. . 3
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5 | 2, 4 | impbid 183 |
. 2
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6 | bi1 178 |
. . . 4
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7 | 6 | pm2.86d 93 |
. . 3
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8 | bi2 189 |
. . . 4
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9 | 8 | pm2.86d 93 |
. . 3
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10 | 7, 9 | impbidd 181 |
. 2
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11 | 5, 10 | impbii 180 |
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 |
This theorem depends on definitions: df-bi 177 |
This theorem is referenced by: pm5.74i 236 pm5.74ri 237 pm5.74d 238 pm5.74rd 239 bibi2d 309 pm5.32 617 orbidi 898 |
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