Description: Compact quantifier-free version of the standard definition df-fin . (Contributed by Stefan O'Rear, 6-Jan-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | dffin1-5 | |- Fin = ( ~~ " _om ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ensymb | |- ( x ~~ y <-> y ~~ x ) |
|
2 | 1 | rexbii | |- ( E. y e. _om x ~~ y <-> E. y e. _om y ~~ x ) |
3 | 2 | abbii | |- { x | E. y e. _om x ~~ y } = { x | E. y e. _om y ~~ x } |
4 | df-fin | |- Fin = { x | E. y e. _om x ~~ y } |
|
5 | dfima2 | |- ( ~~ " _om ) = { x | E. y e. _om y ~~ x } |
|
6 | 3 4 5 | 3eqtr4i | |- Fin = ( ~~ " _om ) |