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Mirrors > Home > ILE Home > Th. List > pm5.21ndd | Unicode version |
Description: Eliminate an antecedent implied by each side of a biconditional, deduction version. (Contributed by Paul Chapman, 21-Nov-2012.) (Revised by Mario Carneiro, 31-Jan-2015.) |
Ref | Expression |
---|---|
pm5.21ndd.1 |
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pm5.21ndd.2 |
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pm5.21ndd.3 |
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Ref | Expression |
---|---|
pm5.21ndd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm5.21ndd.1 |
. . . 4
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2 | pm5.21ndd.3 |
. . . 4
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3 | 1, 2 | syld 44 |
. . 3
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4 | 3 | ibd 176 |
. 2
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5 | pm5.21ndd.2 |
. . . . 5
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6 | 5, 2 | syld 44 |
. . . 4
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7 | bicom1 129 |
. . . 4
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8 | 6, 7 | syl6 33 |
. . 3
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9 | 8 | ibd 176 |
. 2
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10 | 4, 9 | impbid 127 |
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: pm5.21nd 863 sbcrext 2916 rmob 2931 epelg 4117 eqbrrdva 4606 relbrcnvg 4811 fmptco 5464 ovelrn 5793 brtpos2 6016 elpmg 6421 brdomg 6465 genpelvl 7071 genpelvu 7072 fzoval 9559 clim 10669 |
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