Theorem syli 33

Description: Syllogism inference with common nested antecedent. (Contributed by NM, 4-Nov-2004.)

Hypotheses

Ref	Expression
syli.1	|- ( ps -> ( ph -> ch ) )
syli.2	|- ( ch -> ( ph -> th ) )

Assertion

Ref	Expression
syli	|- ( ps -> ( ph -> th ) )

Proof of Theorem syli

Step	Hyp	Ref	Expression
1		syli.1	. 2 |- ( ps -> ( ph -> ch ) )
2		syli.2	. . 3 |- ( ch -> ( ph -> th ) )
3	2	com12 27	. 2 |- ( ph -> ( ch -> th ) )
4	1, 3	sylcom 25	1 |- ( ps -> ( ph -> th ) )

Syntax hints:   -> wi 4

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

This theorem is referenced by:  ibd  167  bijadc  776  sbi2v  1772  elab3gf  2692  elreldm  4560  tz6.12c  5203  rntpos  5872  smores  5907  f1domg  6238  negm  8550