Theorem 3simpc 1027

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 1014	. 2 |- ( ( ph /\ ps /\ ch ) <-> ( ps /\ ch /\ ph ) )
2		3simpa 1025	. 2 |- ( ( ps /\ ch /\ ph ) -> ( ps /\ ch ) )
3	1, 2	sylbi 121	1 |- ( ( ph /\ ps /\ ch ) -> ( ps /\ ch ) )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104   /\ w3a 1009

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117  df-3an 1011

This theorem is used by:  simp3  1030  3adant1  1046  3adantl1  1184  3adantr1  1187  eupickb  2168  find  4746  fovcld  6193  fisseneq  7242  eqsupti  7337  divcanap2  9013  diveqap0  9015  divrecap  9021  divcanap3  9031  eliooord  10341  fzrev3  10505  sqdivap  11055  swrdlend  11446  swrdnd  11447  ccats1pfxeqbi  11530  muldvds2  12603  dvdscmul  12604  dvdsmulc  12605  dvdstr  12614  rng1zr  14311  srg1zr  14343  domneq0  14633  znleval2  15041  aspid  15069  cncfmptc  15750  cnplimclemr  15823  uhgr2edg  16575  umgr2edgneu  16581  clwwlknp  16786