Theorem imim3i 55

Description: Inference adding three nested antecedents. (Contributed by NM, 19-Dec-2006.)

Hypothesis

Ref	Expression
imim3i.1	|- (ph -> (ps -> ch))

Assertion

Ref	Expression
imim3i	|- ((th -> ph) -> ((th -> ps) -> (th -> ch)))

Proof of Theorem imim3i

Step	Hyp	Ref	Expression
1		imim3i.1	. . 3 |- (ph -> (ps -> ch))
2	1	imim2i 13	. 2 |- ((th -> ph) -> (th -> (ps -> ch)))
3	2	a2d 23	1 |- ((th -> 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:  pm2.83  71  pm5.74  235  bi3ant  280  pm3.43i  442  ax12olem3  1929  ceqsalt  2882