Metamath Proof Explorer


Theorem unipr

Description: The union of a pair is the union of its members. Proposition 5.7 of TakeutiZaring p. 16. (Contributed by NM, 23-Aug-1993) (Proof shortened by BJ, 1-Sep-2024)

Ref Expression
Hypotheses unipr.1
|- A e. _V
unipr.2
|- B e. _V
Assertion unipr
|- U. { A , B } = ( A u. B )

Proof

Step Hyp Ref Expression
1 unipr.1
 |-  A e. _V
2 unipr.2
 |-  B e. _V
3 uniprg
 |-  ( ( A e. _V /\ B e. _V ) -> U. { A , B } = ( A u. B ) )
4 1 2 3 mp2an
 |-  U. { A , B } = ( A u. B )