Description: An infimum is a set. (Contributed by AV, 2-Sep-2020)
Ref | Expression | ||
---|---|---|---|
Hypothesis | infexd.1 | |- ( ph -> R Or A ) |
|
Assertion | infexd | |- ( ph -> inf ( B , A , R ) e. _V ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | infexd.1 | |- ( ph -> R Or A ) |
|
2 | df-inf | |- inf ( B , A , R ) = sup ( B , A , `' R ) |
|
3 | cnvso | |- ( R Or A <-> `' R Or A ) |
|
4 | 1 3 | sylib | |- ( ph -> `' R Or A ) |
5 | 4 | supexd | |- ( ph -> sup ( B , A , `' R ) e. _V ) |
6 | 2 5 | eqeltrid | |- ( ph -> inf ( B , A , R ) e. _V ) |