Theorem imim1d 69

Description: Deduction adding nested consequents. (Contributed by NM, 3-Apr-1994.) (Proof shortened by Wolf Lammen, 12-Sep-2012.)

Hypothesis

Ref	Expression
imim1d.1	|- (ph -> (ps -> ch))

Assertion

Ref	Expression
imim1d	|- (ph -> ((ch -> th) -> (ps -> th)))

Proof of Theorem imim1d

Step	Hyp	Ref	Expression
1		imim1d.1	. 2 |- (ph -> (ps -> ch))
2		idd 21	. 2 |- (ph -> (th -> th))
3	1, 2	imim12d 68	1 |- (ph -> ((ch -> th) -> (ps -> th)))

Syntax hints:   -> wi 4

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

This theorem is referenced by:  imim1  70  imbi1d  220  expt  582  hbimd  1462  moim  1961  moimv  1963  sstr2  2946  ssralv  2998  soss  4042  prarloclem3  6480  fzind  8129  iseqfveq2  8905  setindft  9425