Theorem pm3.3 460

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 452	1 |- ( ( ( ph /\ ps ) -> ch ) -> ( ph -> ( ps -> ch ) ) )

Syntax hints:   -> wi 4   /\ wa 384

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 197  df-an 386

This theorem is referenced by:  impexp  462  pm4.79  607  trer  32310  bj-alanim  32596  bj-mo3OLD  32832  wl-mo3t  33358  trsbc  38750  simplbi2VD  39081  exbirVD  39088  exbiriVD  39089  3impexpVD  39091  trsbcVD  39113  simplbi2comtVD  39124