Theorem imim12d 74

Description: Deduction combining antecedents and consequents. (Contributed by NM, 7-Aug-1994.) (Proof shortened by O'Cat, 30-Oct-2011.)

Hypotheses

Ref	Expression
imim12d.1	|- ( ph -> ( ps -> ch ) )
imim12d.2	|- ( ph -> ( th -> ta ) )

Assertion

Ref	Expression
imim12d	|- ( ph -> ( ( ch -> th ) -> ( ps -> ta ) ) )

Proof of Theorem imim12d

Step	Hyp	Ref	Expression
1		imim12d.1	. 2 |- ( ph -> ( ps -> ch ) )
2		imim12d.2	. . 3 |- ( ph -> ( th -> ta ) )
3	2	imim2d 54	. 2 |- ( ph -> ( ( ch -> th ) -> ( ch -> ta ) ) )
4	1, 3	syl5d 68	1 |- ( ph -> ( ( ch -> th ) -> ( ps -> ta ) ) )

Syntax hints:   -> wi 4

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

This theorem is referenced by:  imim1d  75  equveli  1759  hbsb4t  2013  mo23  2067  rspcimdv  2844  r19.29uz  11003  txlm  13864  metcnpi3  14102  addcncntoplem  14136  cnplimcim  14221  setindis  14804  bdsetindis  14806  bj-findis  14816