Description: Hypothesis for weak deduction theorem to eliminate A =/= 0 . (Contributed by NM, 15-May-1999)
Ref | Expression | ||
---|---|---|---|
Assertion | elimne0 | |- if ( A =/= 0 , A , 1 ) =/= 0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | neeq1 | |- ( A = if ( A =/= 0 , A , 1 ) -> ( A =/= 0 <-> if ( A =/= 0 , A , 1 ) =/= 0 ) ) |
|
2 | neeq1 | |- ( 1 = if ( A =/= 0 , A , 1 ) -> ( 1 =/= 0 <-> if ( A =/= 0 , A , 1 ) =/= 0 ) ) |
|
3 | ax-1ne0 | |- 1 =/= 0 |
|
4 | 1 2 3 | elimhyp | |- if ( A =/= 0 , A , 1 ) =/= 0 |