Theorem 3simpc 998

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 985	. 2 |- ( ( ph /\ ps /\ ch ) <-> ( ps /\ ch /\ ph ) )
2		3simpa 996	. 2 |- ( ( ps /\ ch /\ ph ) -> ( ps /\ ch ) )
3	1, 2	sylbi 121	1 |- ( ( ph /\ ps /\ ch ) -> ( ps /\ ch ) )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 980

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 982

This theorem is referenced by:  simp3  1001  3adant1  1017  3adantl1  1155  3adantr1  1158  eupickb  2134  find  4646  fovcld  6049  fisseneq  7030  eqsupti  7097  divcanap2  8752  diveqap0  8754  divrecap  8760  divcanap3  8770  eliooord  10049  fzrev3  10208  sqdivap  10746  muldvds2  12070  dvdscmul  12071  dvdsmulc  12072  dvdstr  12081  domneq0  13976  znleval2  14358  cncfmptc  15010  cnplimclemr  15083