Theorem syl3anl1 1374

Description: A syllogism inference. (Contributed by NM, 24-Feb-2005.)

Hypotheses

Ref	Expression
syl3anl1.1	|- ( ph -> ps )
syl3anl1.2	|- ( ( ( ps /\ ch /\ th ) /\ ta ) -> et )

Assertion

Ref	Expression
syl3anl1	|- ( ( ( ph /\ ch /\ th ) /\ ta ) -> et )

Proof of Theorem syl3anl1

Step	Hyp	Ref	Expression
1		syl3anl1.1	. . 3 |- ( ph -> ps )
2	1	3anim1i 1248	. 2 |- ( ( ph /\ ch /\ th ) -> ( ps /\ ch /\ th ) )
3		syl3anl1.2	. 2 |- ( ( ( ps /\ ch /\ th ) /\ ta ) -> et )
4	2, 3	sylan 488	1 |- ( ( ( ph /\ ch /\ th ) /\ ta ) -> et )

Syntax hints:   -> wi 4   /\ wa 384   /\ w3a 1037

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 197  df-an 386  df-3an 1039

This theorem is referenced by:  suprzcl  11457  latjcom  17059  latmcom  17075  ring1zr  19275  lgsdinn0  25070  crngohomfo  33805  dalem53  35011