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  7246  eqsupti  7342  divcanap2  9018  diveqap0  9020  divrecap  9026  divcanap3  9036  eliooord  10347  fzrev3  10511  sqdivap  11061  swrdlend  11452  swrdnd  11453  ccats1pfxeqbi  11536  muldvds2  12609  dvdscmul  12610  dvdsmulc  12611  dvdstr  12620  rng1zr  14366  srg1zr  14398  domneq0  14690  znleval2  15098  aspid  15126  cncfmptc  15822  cnplimclemr  15895  uhgr2edg  16652  umgr2edgneu  16658  clwwlknp  16863