Theorem syl3anl1 1183

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 1090	. 2 |- ( ( ph /\ ch /\ th ) -> ( ps /\ ch /\ th ) )
3		syl3anl1.2	. 2 |- ( ( ( ps /\ ch /\ th ) /\ ta ) -> et )
4	2, 3	sylan 267	1 |- ( ( ( ph /\ ch /\ th ) /\ ta ) -> et )

Syntax hints:   -> wi 4   /\ wa 97   /\ w3a 885

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110  df-3an 887

This theorem is referenced by: (None)