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 12	. 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-1 5  ax-2 6  ax-mp 7

This theorem is referenced by:  pm2.83  71  pm5.74  168  bi3ant  213  pm3.43i  258  ceqsalt  2580