Theorem syl2ani 637

Description: A syllogism inference. (Contributed by NM, 3-Aug-1999.)

Hypotheses

Ref	Expression
syl2ani.1	|- (ph -> ch)
syl2ani.2	|- (et -> th)
syl2ani.3	|- (ps -> ((ch /\ th) -> ta))

Assertion

Ref	Expression
syl2ani	|- (ps -> ((ph /\ et) -> ta))

Proof of Theorem syl2ani

Step	Hyp	Ref	Expression
1		syl2ani.1	. 2 |- (ph -> ch)
2		syl2ani.2	. . 3 |- (et -> th)
3		syl2ani.3	. . 3 |- (ps -> ((ch /\ th) -> ta))
4	2, 3	sylan2i 636	. 2 |- (ps -> ((ch /\ et) -> ta))
5	1, 4	sylani 635	1 |- (ps -> ((ph /\ et) -> ta))

Syntax hints:   -> wi 4   /\ wa 358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360

This theorem is referenced by: (None)