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  9012  diveqap0  9014  divrecap  9020  divcanap3  9030  eliooord  10340  fzrev3  10504  sqdivap  11053  swrdlend  11444  swrdnd  11445  ccats1pfxeqbi  11528  muldvds2  12600  dvdscmul  12601  dvdsmulc  12602  dvdstr  12611  rng1zr  14308  srg1zr  14340  domneq0  14630  znleval2  15038  aspid  15066  cncfmptc  15746  cnplimclemr  15819  uhgr2edg  16545  umgr2edgneu  16551  clwwlknp  16756