Theorem imim2d 48

Description: Deduction adding nested antecedents. (Contributed by NM, 5-Aug-1993.)

Hypothesis

Ref	Expression
imim2d.1	|- (ph -> (ps -> ch))

Assertion

Ref	Expression
imim2d	|- (ph -> ((th -> ps) -> (th -> ch)))

Proof of Theorem imim2d

Step	Hyp	Ref	Expression
1		imim2d.1	. . 3 |- (ph -> (ps -> ch))
2	1	a1d 22	. 2 |- (ph -> (th -> (ps -> ch)))
3	2	a2d 23	1 |- (ph -> ((th -> ps) -> (th -> ch)))

Syntax hints:   -> wi 4

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

This theorem is referenced by:  imim2  49  embantd  50  imim12d  68  anc2r  539  pm5.31  571  dedlem0b  919  nic-ax  1438  nic-axALT  1439  19.23t  1800  nfimd  1808  spimt  1974  ssuni  3914  weds  5939  spacind  6288