Theorem pm10.56 38569

Description: Theorem *10.56 in [WhiteheadRussell] p. 156. (Contributed by Andrew Salmon, 24-May-2011.)

Assertion

Ref	Expression
pm10.56	|- ( ( A. x ( ph -> ps ) /\ E. x ( ph /\ ch ) ) -> E. x ( ps /\ ch ) )

Proof of Theorem pm10.56

Step	Hyp	Ref	Expression
1		pm3.45 879	. . 3 |- ( ( ph -> ps ) -> ( ( ph /\ ch ) -> ( ps /\ ch ) ) )
2	1	aleximi 1759	. 2 |- ( A. x ( ph -> ps ) -> ( E. x ( ph /\ ch ) -> E. x ( ps /\ ch ) ) )
3	2	imp 445	1 |- ( ( A. x ( ph -> ps ) /\ E. x ( ph /\ ch ) ) -> E. x ( ps /\ ch ) )

Syntax hints:   -> wi 4   /\ wa 384   A.wal 1481   E.wex 1704

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  df-ex 1705

This theorem is referenced by: (None)