Theorem syl3anl2 1375

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

Hypotheses

Ref	Expression
syl3anl2.1	|- ( ph -> ch )
syl3anl2.2	|- ( ( ( ps /\ ch /\ th ) /\ ta ) -> et )

Assertion

Ref	Expression
syl3anl2	|- ( ( ( ps /\ ph /\ th ) /\ ta ) -> et )

Proof of Theorem syl3anl2

Step	Hyp	Ref	Expression
1		syl3anl2.1	. . 3 |- ( ph -> ch )
2		syl3anl2.2	. . . 4 |- ( ( ( ps /\ ch /\ th ) /\ ta ) -> et )
3	2	ex 450	. . 3 |- ( ( ps /\ ch /\ th ) -> ( ta -> et ) )
4	1, 3	syl3an2 1360	. 2 |- ( ( ps /\ ph /\ th ) -> ( ta -> et ) )
5	4	imp 445	1 |- ( ( ( ps /\ ph /\ 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:  syl3anr2  1379  chfacfscmulcl  20662  chfacfscmulgsum  20665  chfacfpmmulcl  20666  chfacfpmmulgsum  20669  cpmadumatpolylem1  20686  cpmadumatpolylem2  20687  cpmadumatpoly  20688  chcoeffeqlem  20690  2atlt  34725