Theorem 3simpc 1023

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 1010	. 2 |- ( ( ph /\ ps /\ ch ) <-> ( ps /\ ch /\ ph ) )
2		3simpa 1021	. 2 |- ( ( ps /\ ch /\ ph ) -> ( ps /\ ch ) )
3	1, 2	sylbi 121	1 |- ( ( ph /\ ps /\ ch ) -> ( ps /\ ch ) )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 1005

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 1007

This theorem is referenced by:  simp3  1026  3adant1  1042  3adantl1  1180  3adantr1  1183  eupickb  2162  find  4721  fovcld  6158  fisseneq  7195  eqsupti  7287  divcanap2  8954  diveqap0  8956  divrecap  8962  divcanap3  8972  eliooord  10261  fzrev3  10421  sqdivap  10965  swrdlend  11350  swrdnd  11351  ccats1pfxeqbi  11434  muldvds2  12503  dvdscmul  12504  dvdsmulc  12505  dvdstr  12514  domneq0  14418  znleval2  14802  cncfmptc  15461  cnplimclemr  15534  uhgr2edg  16201  umgr2edgneu  16207  clwwlknp  16412