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Mirrors > Home > NFE Home > Th. List > 4cases | Unicode version |
Description: Inference eliminating two antecedents from the four possible cases that result from their true/false combinations. (Contributed by NM, 25-Oct-2003.) |
Ref | Expression |
---|---|
4cases.1 |
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4cases.2 |
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4cases.3 |
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4cases.4 |
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Ref | Expression |
---|---|
4cases |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 4cases.1 |
. . 3
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2 | 4cases.3 |
. . 3
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3 | 1, 2 | pm2.61ian 765 |
. 2
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4 | 4cases.2 |
. . 3
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5 | 4cases.4 |
. . 3
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6 | 4, 5 | pm2.61ian 765 |
. 2
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7 | 3, 6 | pm2.61i 156 |
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-an 360 |
This theorem is referenced by: 4casesdan 916 ax11eq 2193 ax11el 2194 |
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