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Mirrors > Home > ILE Home > Th. List > imanst | Unicode version |
Description: Express implication in terms of conjunction. Theorem 3.4(27) of [Stoll] p. 176. (Contributed by NM, 12-Mar-1993.) (Proof shortened by Wolf Lammen, 30-Oct-2012.) |
Ref | Expression |
---|---|
imanst |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | notnot 629 |
. . . 4
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2 | df-stab 831 |
. . . . 5
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3 | 2 | biimpi 120 |
. . . 4
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4 | 1, 3 | impbid2 143 |
. . 3
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5 | 4 | imbi2d 230 |
. 2
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6 | imnan 690 |
. 2
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7 | 5, 6 | bitrdi 196 |
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-in1 614 ax-in2 615 |
This theorem depends on definitions: df-bi 117 df-stab 831 |
This theorem is referenced by: imandc 889 dfss4st 3369 |
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