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  4691  fovcld  6115  fisseneq  7107  eqsupti  7174  divcanap2  8838  diveqap0  8840  divrecap  8846  divcanap3  8856  eliooord  10136  fzrev3  10295  sqdivap  10837  swrdlend  11205  swrdnd  11206  ccats1pfxeqbi  11289  muldvds2  12343  dvdscmul  12344  dvdsmulc  12345  dvdstr  12354  domneq0  14251  znleval2  14633  cncfmptc  15285  cnplimclemr  15358  uhgr2edg  16019  umgr2edgneu  16025