Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > pm5.74 | Structured version Visualization version Unicode version |
Description: Distribution of implication over biconditional. Theorem *5.74 of [WhiteheadRussell] p. 126. (Contributed by NM, 1-Aug-1994.) (Proof shortened by Wolf Lammen, 11-Apr-2013.) |
Ref | Expression |
---|---|
pm5.74 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | biimp 205 | . . . 4 | |
2 | 1 | imim3i 64 | . . 3 |
3 | biimpr 210 | . . . 4 | |
4 | 3 | imim3i 64 | . . 3 |
5 | 2, 4 | impbid 202 | . 2 |
6 | biimp 205 | . . . 4 | |
7 | 6 | pm2.86d 107 | . . 3 |
8 | biimpr 210 | . . . 4 | |
9 | 8 | pm2.86d 107 | . . 3 |
10 | 7, 9 | impbidd 200 | . 2 |
11 | 5, 10 | impbii 199 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 197 |
This theorem is referenced by: pm5.74i 260 pm5.74ri 261 pm5.74d 262 pm5.74rd 263 bibi2d 332 pm5.32 668 orbidi 973 |
Copyright terms: Public domain | W3C validator |