Theorem 3simpc 1020

Description: Simplification of triple conjunction. (Contributed by NM, 21-Apr-1994.) (Proof shortened by Andrew Salmon, 13-May-2011.)

Assertion

Ref	Expression
3simpc	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → (𝜓 ∧ 𝜒))

Proof of Theorem 3simpc

Step	Hyp	Ref	Expression
1		3anrot 1007	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) ↔ (𝜓 ∧ 𝜒 ∧ 𝜑))
2		3simpa 1018	. 2 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜑) → (𝜓 ∧ 𝜒))
3	1, 2	sylbi 121	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → (𝜓 ∧ 𝜒))

Syntax hints:   → wi 4   ∧ wa 104   ∧ w3a 1002

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 1004

This theorem is referenced by:  simp3  1023  3adant1  1039  3adantl1  1177  3adantr1  1180  eupickb  2159  find  4691  fovcld  6115  fisseneq  7104  eqsupti  7171  divcanap2  8835  diveqap0  8837  divrecap  8843  divcanap3  8853  eliooord  10132  fzrev3  10291  sqdivap  10833  swrdlend  11198  swrdnd  11199  ccats1pfxeqbi  11282  muldvds2  12336  dvdscmul  12337  dvdsmulc  12338  dvdstr  12347  domneq0  14244  znleval2  14626  cncfmptc  15278  cnplimclemr  15351  uhgr2edg  16012  umgr2edgneu  16018