Theorem syli 37

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 30	. 2 |- ( ph -> ( ch -> th ) )
4	1, 3	sylcom 28	1 |- ( ps -> ( ph -> 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:  ibd  177  bijadc  867  sbi2v  1864  elab3gf  2834  elreldm  4765  tz6.12c  5451  rntpos  6154  smores  6189  f1domg  6652  negm  9407