Metamath Proof Explorer

Theorem elec

Description: Membership in an equivalence class. Theorem 72 of Suppes p. 82. (Contributed by NM, 23-Jul-1995)

Ref Expression
Hypotheses elec.1 
|- A e. _V
elec.2 
|- B e. _V
Assertion elec 
|- ( A e. [ B ] R <-> B R A )

Proof

Step Hyp Ref Expression
1 elec.1 
 |-  A e. _V
2 elec.2 
 |-  B e. _V
3 elecg 
 |-  ( ( A e. _V /\ B e. _V ) -> ( A e. [ B ] R <-> B R A ) )
4 1 2 3 mp2an 
 |-  ( A e. [ B ] R <-> B R A )