Theorem 3simpc 1022

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 1009	. 2 |- ( ( ph /\ ps /\ ch ) <-> ( ps /\ ch /\ ph ) )
2		3simpa 1020	. 2 |- ( ( ps /\ ch /\ ph ) -> ( ps /\ ch ) )
3	1, 2	sylbi 121	1 |- ( ( ph /\ ps /\ ch ) -> ( ps /\ ch ) )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 1004

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 1006

This theorem is referenced by:  simp3  1025  3adant1  1041  3adantl1  1179  3adantr1  1182  eupickb  2161  find  4697  fovcld  6125  fisseneq  7126  eqsupti  7194  divcanap2  8859  diveqap0  8861  divrecap  8867  divcanap3  8877  eliooord  10162  fzrev3  10321  sqdivap  10864  swrdlend  11238  swrdnd  11239  ccats1pfxeqbi  11322  muldvds2  12377  dvdscmul  12378  dvdsmulc  12379  dvdstr  12388  domneq0  14285  znleval2  14667  cncfmptc  15319  cnplimclemr  15392  uhgr2edg  16056  umgr2edgneu  16062  clwwlknp  16267