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  4748  fovcld  6196  fisseneq  7248  eqsupti  7342  divcanap2  9018  diveqap0  9020  divrecap  9026  divcanap3  9036  eliooord  10346  fzrev3  10510  sqdivap  11060  swrdlend  11451  swrdnd  11452  ccats1pfxeqbi  11535  muldvds2  12608  dvdscmul  12609  dvdsmulc  12610  dvdstr  12619  rng1zr  14365  srg1zr  14397  domneq0  14689  znleval2  15097  aspid  15125  cncfmptc  15839  cnplimclemr  15912  uhgr2edg  16669  umgr2edgneu  16675  clwwlknp  16880