Metamath Proof Explorer


Theorem infex

Description: An infimum is a set. (Contributed by AV, 3-Sep-2020)

Ref Expression
Hypothesis infex.1
|- R Or A
Assertion infex
|- inf ( B , A , R ) e. _V

Proof

Step Hyp Ref Expression
1 infex.1
 |-  R Or A
2 id
 |-  ( R Or A -> R Or A )
3 2 infexd
 |-  ( R Or A -> inf ( B , A , R ) e. _V )
4 1 3 ax-mp
 |-  inf ( B , A , R ) e. _V