Theorem albitr 38562

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

Assertion

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

Proof of Theorem albitr

Step	Hyp	Ref	Expression
1		bitr 745	. 2 |- ( ( ( ph <-> ps ) /\ ( ps <-> ch ) ) -> ( ph <-> ch ) )
2	1	alanimi 1744	1 |- ( ( A. x ( ph <-> ps ) /\ A. x ( ps <-> ch ) ) -> A. x ( ph <-> ch ) )

Syntax hints:   -> wi 4   <-> wb 196   /\ wa 384   A.wal 1481

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737

This theorem depends on definitions:  df-bi 197  df-an 386

This theorem is referenced by: (None)