Theorem simp2l3 1162

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Assertion

Ref	Expression
simp2l3	|- ( ( ta /\ ( ( ph /\ ps /\ ch ) /\ th ) /\ et ) -> ch )

Proof of Theorem simp2l3

Step	Hyp	Ref	Expression
1		simpl3 1066	. 2 |- ( ( ( ph /\ ps /\ ch ) /\ th ) -> ch )
2	1	3ad2ant2 1083	1 |- ( ( ta /\ ( ( ph /\ ps /\ ch ) /\ th ) /\ et ) -> ch )

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:  btwnconn1lem8  32201  btwnconn1lem12  32205  2lplnja  34905  cdlemk21-2N  36179  cdlemk19xlem  36230  jm2.27  37575