Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > mpan10 | Unicode version |
Description: Modus ponens mixed with several conjunctions. (Contributed by Jim Kingdon, 7-Jan-2018.) |
Ref | Expression |
---|---|
mpan10 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ancom 262 | . . . 4 | |
2 | 1 | anbi2i 444 | . . 3 |
3 | anass 393 | . . 3 | |
4 | anass 393 | . . 3 | |
5 | 2, 3, 4 | 3bitr4i 210 | . 2 |
6 | id 19 | . . . 4 | |
7 | 6 | imp 122 | . . 3 |
8 | 7 | anim1i 333 | . 2 |
9 | 5, 8 | sylbi 119 | 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 depends on definitions: df-bi 115 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |