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-mp 5  ax-1 6  ax-2 7

This theorem is referenced by:  ibd  234  bija  344  eqpw1uni  4331  iss  5001  tz6.12c  5348