Theorem syl3anl3 1278

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

Hypotheses

Ref	Expression
syl3anl3.1	|- ( ph -> th )
syl3anl3.2	|- ( ( ( ps /\ ch /\ th ) /\ ta ) -> et )

Assertion

Ref	Expression
syl3anl3	|- ( ( ( ps /\ ch /\ ph ) /\ ta ) -> et )

Proof of Theorem syl3anl3

Step	Hyp	Ref	Expression
1		syl3anl3.1	. . 3 |- ( ph -> th )
2	1	3anim3i 1177	. 2 |- ( ( ps /\ ch /\ ph ) -> ( ps /\ ch /\ th ) )
3		syl3anl3.2	. 2 |- ( ( ( ps /\ ch /\ th ) /\ ta ) -> et )
4	2, 3	sylan 281	1 |- ( ( ( ps /\ ch /\ ph ) /\ ta ) -> et )

Syntax hints:   -> wi 4   /\ wa 103   /\ w3a 968

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116  df-3an 970

This theorem is referenced by:  lgsdirnn0  13588