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  7336  divcanap2  9010  diveqap0  9012  divrecap  9018  divcanap3  9028  eliooord  10330  fzrev3  10494  sqdivap  11040  swrdlend  11430  swrdnd  11431  ccats1pfxeqbi  11514  muldvds2  12584  dvdscmul  12585  dvdsmulc  12586  dvdstr  12595  rng1zr  14259  srg1zr  14291  domneq0  14581  znleval2  14989  aspid  15017  cncfmptc  15697  cnplimclemr  15770  uhgr2edg  16447  umgr2edgneu  16453  clwwlknp  16658