Theorem 3simpc 1020

Description: Simplification of triple conjunction. (Contributed by NM, 21-Apr-1994.) (Proof shortened by Andrew Salmon, 13-May-2011.)

Assertion

Ref	Expression
3simpc	|- ( ( ph /\ ps /\ ch ) -> ( ps /\ ch ) )

Proof of Theorem 3simpc

Step	Hyp	Ref	Expression
1		3anrot 1007	. 2 |- ( ( ph /\ ps /\ ch ) <-> ( ps /\ ch /\ ph ) )
2		3simpa 1018	. 2 |- ( ( ps /\ ch /\ ph ) -> ( ps /\ ch ) )
3	1, 2	sylbi 121	1 |- ( ( ph /\ ps /\ ch ) -> ( ps /\ ch ) )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 1002

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-3an 1004

This theorem is referenced by:  simp3  1023  3adant1  1039  3adantl1  1177  3adantr1  1180  eupickb  2159  find  4690  fovcld  6108  fisseneq  7092  eqsupti  7159  divcanap2  8823  diveqap0  8825  divrecap  8831  divcanap3  8841  eliooord  10120  fzrev3  10279  sqdivap  10820  swrdlend  11185  swrdnd  11186  ccats1pfxeqbi  11269  muldvds2  12323  dvdscmul  12324  dvdsmulc  12325  dvdstr  12334  domneq0  14230  znleval2  14612  cncfmptc  15264  cnplimclemr  15337  uhgr2edg  15998  umgr2edgneu  16004