Metamath Proof Explorer

Theorem albitr

Description: Theorem *10.301 in WhiteheadRussell p. 151. (Contributed by Andrew Salmon, 24-May-2011)

Ref Expression
Assertion albitr 
|- ( ( A. x ( ph <-> ps ) /\ A. x ( ps <-> ch ) ) -> A. x ( ph <-> ch ) )

Proof

Step Hyp Ref Expression
1 bitr 
 |-  ( ( ( ph <-> ps ) /\ ( ps <-> ch ) ) -> ( ph <-> ch ) )
2 1 alanimi 
 |-  ( ( A. x ( ph <-> ps ) /\ A. x ( ps <-> ch ) ) -> A. x ( ph <-> ch ) )