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Mirrors > Home > ILE Home > Th. List > 3anandirs | Unicode version |
Description: Inference that undistributes a triple conjunction in the antecedent. (Contributed by NM, 25-Jul-2006.) (Revised by NM, 18-Apr-2007.) |
Ref | Expression |
---|---|
3anandirs.1 |
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Ref | Expression |
---|---|
3anandirs |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl1 1000 |
. 2
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2 | simpr 110 |
. 2
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3 | simpl2 1001 |
. 2
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4 | simpl3 1002 |
. 2
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5 | 3anandirs.1 |
. 2
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6 | 1, 2, 3, 2, 4, 2, 5 | syl222anc 1254 |
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 |
This theorem depends on definitions: df-bi 117 df-3an 980 |
This theorem is referenced by: (None) |
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