Theorem imim3i 19

Description: Inference adding three nested antecedents.

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 17	. 2 |- ((th -> ph) -> (th -> (ps -> ch)))
3	2	a2d 13	1 |- ((th -> ph) -> ((th -> ps) -> (th -> ch)))

Syntax hints:   -> wi 3

This theorem is referenced by:  pm2.83 31  pm3.43i 287  pm5.74 583  iscms2lem4 7992

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-mp 7

Copyright terms: Public domain