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  2123  find  4631  fovcld  6023  fisseneq  6988  eqsupti  7055  divcanap2  8699  diveqap0  8701  divrecap  8707  divcanap3  8717  eliooord  9994  fzrev3  10153  sqdivap  10674  muldvds2  11960  dvdscmul  11961  dvdsmulc  11962  dvdstr  11971  domneq0  13768  znleval2  14142  cncfmptc  14750  cnplimclemr  14823