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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 298 | . 2 |
3 | mpanr2.2 | . 2 | |
4 | 2, 3 | sylan2 270 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 |
This theorem is referenced by: op1steq 5805 prarloclemarch2 6517 prarloclemlt 6591 prsradd 6870 muleqadd 7649 divdivap1 7699 addltmul 8161 elfzp1b 8959 elfzm1b 8960 expp1zap 9303 expm1ap 9304 |
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