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Mirrors > Home > ILE Home > Th. List > mpanl2 | Unicode version |
Description: An inference based on modus ponens. (Contributed by NM, 16-Aug-1994.) (Proof shortened by Andrew Salmon, 7-May-2011.) |
Ref | Expression |
---|---|
mpanl2.1 |
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mpanl2.2 |
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Ref | Expression |
---|---|
mpanl2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mpanl2.1 |
. . 3
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2 | 1 | jctr 313 |
. 2
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3 | mpanl2.2 |
. 2
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4 | 2, 3 | sylan 281 |
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 105 ax-ia2 106 ax-ia3 107 |
This theorem is referenced by: mpanr1 434 mp3an2 1304 reuss 3362 tfri3 6272 prarloclemarch2 7251 prarloclemlt 7325 prsradd 7618 map2psrprg 7637 pitonnlem2 7679 axcnre 7713 muleqadd 8453 divdivap2 8508 addltmul 8980 |
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