Theorem a1i13 27

Description: Add two antecedents to a wff. (Contributed by Jeff Hankins, 4-Aug-2009.)

Hypothesis

Ref	Expression
a1i13.1	|- ( ps -> th )

Assertion

Ref	Expression
a1i13	|- ( ph -> ( ps -> ( ch -> th ) ) )

Proof of Theorem a1i13

Step	Hyp	Ref	Expression
1		a1i13.1	. . 3 |- ( ps -> th )
2	1	a1d 25	. 2 |- ( ps -> ( ch -> th ) )
3	2	a1i 11	1 |- ( ph -> ( ps -> ( ch -> th ) ) )

Syntax hints:   -> wi 4

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

This theorem is referenced by:  ad4ant24  1298  ad5ant245  1307  seqshft2  12827  seqsplit  12834  filconn  21687  usgr2pth  26660  elwspths2on  26853  frgr3vlem1  27137  3vfriswmgrlem  27141