Theorem alsyl 1820

Description: Universally quantified and uncurried (imported) form of syllogism. Theorem *10.3 in [WhiteheadRussell] p. 150. (Contributed by Andrew Salmon, 8-Jun-2011.)

Assertion

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

Proof of Theorem alsyl

Step	Hyp	Ref	Expression
1		pm3.33 609	. 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   /\ 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:  barbara  2563