Theorem pm3.3 451

Description: Theorem *3.3 (Exp) of [WhiteheadRussell] p. 112. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 24-Mar-2013.)

Assertion

Ref	Expression
pm3.3	|- ( ( ( ph /\ ps ) -> ch ) -> ( ph -> ( ps -> ch ) ) )

Proof of Theorem pm3.3

Step	Hyp	Ref	Expression
1		id 22	. 2 |- ( ( ( ph /\ ps ) -> ch ) -> ( ( ph /\ ps ) -> ch ) )
2	1	expd 443	1 |- ( ( ( ph /\ ps ) -> ch ) -> ( ph -> ( ps -> ch ) ) )

Syntax hints:   -> wi 4   /\ wa 376

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

This theorem depends on definitions:  df-bi 190  df-an 378

This theorem is referenced by:  impexp  453  pm4.79  593  trer  31043  bj-alanim  31268  bj-mo3OLD  31515  wl-mo3t  31975  trsbc  36971  simplbi2VD  37305  exbirVD  37312  exbiriVD  37313  3impexpVD  37315  trsbcVD  37337  simplbi2comtVD  37348