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Mirrors > Home > ILE Home > Th. List > mpanr2 | Unicode version |
Description: An inference based on modus ponens. (Contributed by NM, 3-May-1994.) (Proof shortened by Andrew Salmon, 7-May-2011.) (Proof shortened by Wolf Lammen, 7-Apr-2013.) |
Ref | Expression |
---|---|
mpanr2.1 | |
mpanr2.2 |
Ref | Expression |
---|---|
mpanr2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mpanr2.1 | . . 3 | |
2 | 1 | jctr 308 | . 2 |
3 | mpanr2.2 | . 2 | |
4 | 2, 3 | sylan2 280 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 |
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: op1steq 5825 pm54.43 6459 prarloclemarch2 6609 prarloclemlt 6683 prsradd 6962 muleqadd 7758 divdivap1 7811 addltmul 8267 elfzp1b 9114 elfzm1b 9115 expp1zap 9525 expm1ap 9526 |
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