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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 | |
mpanr12.2 | |
mpanr12.3 |
Ref | Expression |
---|---|
mpanr12 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mpanr12.2 | . 2 | |
2 | mpanr12.1 | . . 3 | |
3 | mpanr12.3 | . . 3 | |
4 | 2, 3 | mpanr1 413 | . 2 |
5 | 1, 4 | mpan2 401 | 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: 2dom 6285 phplem4 6318 mulidnq 6487 nq0m0r 6554 nq0a0 6555 addpinq1 6562 0idsr 6852 1idsr 6853 00sr 6854 addresr 6913 mulresr 6914 pitonnlem2 6923 ax0id 6952 recexaplem2 7633 reclt1 7862 crap0 7910 nominpos 8162 expnass 9357 crim 9458 sqrt00 9638 mulcn2 9833 |
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