Theorem pm3.3 444

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 436	1 |- ( ( ( ph /\ ps ) -> ch ) -> ( ph -> ( ps -> ch ) ) )

Syntax hints:   -> wi 4   /\ wa 369

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 185  df-an 371

This theorem is referenced by:  impexp  446  pm4.79  583  mo3OLD  2325  wl-mo3t  30226  trer  30339  trsbc  33454  simplbi2VD  33789  exbirVD  33796  exbiriVD  33797  3impexpVD  33799  trsbcVD  33820  simplbi2comtVD  33831  bj-alanim  34347