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Mirrors > Home > NFE Home > Th. List > 3jaao | Unicode version |
Description: Inference conjoining and disjoining the antecedents of three implications. (Contributed by Jeff Hankins, 15-Aug-2009.) (Proof shortened by Andrew Salmon, 13-May-2011.) |
Ref | Expression |
---|---|
3jaao.1 |
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3jaao.2 |
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3jaao.3 |
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Ref | Expression |
---|---|
3jaao |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3jaao.1 |
. . 3
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2 | 1 | 3ad2ant1 976 |
. 2
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3 | 3jaao.2 |
. . 3
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4 | 3 | 3ad2ant2 977 |
. 2
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5 | 3jaao.3 |
. . 3
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6 | 5 | 3ad2ant3 978 |
. 2
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7 | 2, 4, 6 | 3jaod 1246 |
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 df-or 359 df-an 360 df-3or 935 df-3an 936 |
This theorem is referenced by: (None) |
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