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  4636  fovcld  6031  fisseneq  7004  eqsupti  7071  divcanap2  8726  diveqap0  8728  divrecap  8734  divcanap3  8744  eliooord  10022  fzrev3  10181  sqdivap  10714  muldvds2  12001  dvdscmul  12002  dvdsmulc  12003  dvdstr  12012  domneq0  13906  znleval2  14288  cncfmptc  14940  cnplimclemr  15013