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Mirrors > Home > ILE Home > Th. List > mpanr12 | Unicode version |
Description: An inference based on modus ponens. (Contributed by NM, 24-Jul-2009.) |
Ref | Expression |
---|---|
mpanr12.1 |
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mpanr12.2 |
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mpanr12.3 |
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Ref | Expression |
---|---|
mpanr12 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mpanr12.2 |
. 2
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2 | mpanr12.1 |
. . 3
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3 | mpanr12.3 |
. . 3
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4 | 2, 3 | mpanr1 428 |
. 2
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5 | 1, 4 | mpan2 416 |
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 is referenced by: cnvoprab 5934 2dom 6452 phplem4 6501 mulidnq 6851 nq0m0r 6918 nq0a0 6919 addpinq1 6926 0idsr 7216 1idsr 7217 00sr 7218 addresr 7277 mulresr 7278 pitonnlem2 7287 ax0id 7316 recexaplem2 8019 reclt1 8251 crap0 8312 nominpos 8545 expnass 9896 crim 10119 sqrt00 10300 mulcn2 10525 opoe 10675 |
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