Theorem syl2im 34

Description: Replace two antecedents. Implication-only version of syl2an 273. (Contributed by Wolf Lammen, 14-May-2013.)

Hypotheses

Ref	Expression
syl2im.1	|- ( ph -> ps )
syl2im.2	|- ( ch -> th )
syl2im.3	|- ( ps -> ( th -> ta ) )

Assertion

Ref	Expression
syl2im	|- ( ph -> ( ch -> ta ) )

Proof of Theorem syl2im

Step	Hyp	Ref	Expression
1		syl2im.1	. 2 |- ( ph -> ps )
2		syl2im.2	. . 3 |- ( ch -> th )
3		syl2im.3	. . 3 |- ( ps -> ( th -> ta ) )
4	2, 3	syl5 28	. 2 |- ( ps -> ( ch -> ta ) )
5	1, 4	syl 14	1 |- ( ph -> ( ch -> ta ) )

Syntax hints:   -> wi 4

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

This theorem is referenced by:  sylc  56  bi3ant  213  pm3.12dc  865  pm3.13dc  866  nfrimi  1418  vtoclr  4388  funopg  4934  xpiderm  6177  ixxssixx  8771  difelfzle  8992  bj-inf2vnlem1  10095