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	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → (𝜓 ∧ 𝜒))

Proof of Theorem 3simpc

Step	Hyp	Ref	Expression
1		3anrot 985	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) ↔ (𝜓 ∧ 𝜒 ∧ 𝜑))
2		3simpa 996	. 2 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜑) → (𝜓 ∧ 𝜒))
3	1, 2	sylbi 121	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → (𝜓 ∧ 𝜒))

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  2126  find  4635  fovcld  6027  fisseneq  6995  eqsupti  7062  divcanap2  8707  diveqap0  8709  divrecap  8715  divcanap3  8725  eliooord  10003  fzrev3  10162  sqdivap  10695  muldvds2  11982  dvdscmul  11983  dvdsmulc  11984  dvdstr  11993  domneq0  13828  znleval2  14210  cncfmptc  14832  cnplimclemr  14905