Theorem 3simpc 999

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 986	. 2 |- ( ( ph /\ ps /\ ch ) <-> ( ps /\ ch /\ ph ) )
2		3simpa 997	. 2 |- ( ( ps /\ ch /\ ph ) -> ( ps /\ ch ) )
3	1, 2	sylbi 121	1 |- ( ( ph /\ ps /\ ch ) -> ( ps /\ ch ) )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 981

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-3an 983

This theorem is referenced by:  simp3  1002  3adant1  1018  3adantl1  1156  3adantr1  1159  eupickb  2136  find  4655  fovcld  6063  fisseneq  7046  eqsupti  7113  divcanap2  8773  diveqap0  8775  divrecap  8781  divcanap3  8791  eliooord  10070  fzrev3  10229  sqdivap  10770  swrdlend  11134  swrdnd  11135  muldvds2  12203  dvdscmul  12204  dvdsmulc  12205  dvdstr  12214  domneq0  14109  znleval2  14491  cncfmptc  15143  cnplimclemr  15216