Description: If A is not a member of B, but an "if" condition requires it, then the "false" branch results. This is a simple utility to provide a slight shortening and simplification of proofs versus applying iffalse directly in this case. (Contributed by David A. Wheeler, 15-May-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | ifnmfalse | |- ( A e/ B -> if ( A e. B , C , D ) = D ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-nel | |- ( A e/ B <-> -. A e. B ) |
|
2 | iffalse | |- ( -. A e. B -> if ( A e. B , C , D ) = D ) |
|
3 | 1 2 | sylbi | |- ( A e/ B -> if ( A e. B , C , D ) = D ) |