theorem biim1a (a b: wff): $ (~a -> b) -> (a -> b <-> b) $;
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | anr | (~a -> b) /\ (a -> b) -> a -> b |
|
2 | anl | (~a -> b) /\ (a -> b) -> ~a -> b |
|
3 | 1, 2 | casesd | (~a -> b) /\ (a -> b) -> b |
4 | 3 | exp | (~a -> b) -> (a -> b) -> b |
5 | ax_1 | b -> a -> b |
|
6 | 5 | a1i | (~a -> b) -> b -> a -> b |
7 | 4, 6 | ibid | (~a -> b) -> (a -> b <-> b) |