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Mirrors > Home > ILE Home > Th. List > mpanl12 | Unicode version |
Description: An inference based on modus ponens. (Contributed by NM, 13-Jul-2005.) |
Ref | Expression |
---|---|
mpanl12.1 | |
mpanl12.2 | |
mpanl12.3 |
Ref | Expression |
---|---|
mpanl12 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mpanl12.2 | . 2 | |
2 | mpanl12.1 | . . 3 | |
3 | mpanl12.3 | . . 3 | |
4 | 2, 3 | mpanl1 410 | . 2 |
5 | 1, 4 | mpan 400 | 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: reuun1 3219 ordtri2orexmid 4248 opthreg 4280 ordtri2or2exmid 4296 fvtp1 5372 nq0m0r 6554 nq02m 6563 gt0srpr 6833 pitoregt0 6925 axcnre 6955 addgt0 7443 addgegt0 7444 addgtge0 7445 addge0 7446 addgt0i 7480 addge0i 7481 addgegt0i 7482 add20i 7484 mulge0i 7611 recextlem1 7632 recap0 7664 recdivap 7694 recgt1 7863 prodgt0i 7874 prodge0i 7875 iccshftri 8863 iccshftli 8865 iccdili 8867 icccntri 8869 mulexpzap 9295 expaddzap 9299 amgm2 9714 |
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