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  4632  fovcld  6024  fisseneq  6990  eqsupti  7057  divcanap2  8701  diveqap0  8703  divrecap  8709  divcanap3  8719  eliooord  9997  fzrev3  10156  sqdivap  10677  muldvds2  11963  dvdscmul  11964  dvdsmulc  11965  dvdstr  11974  domneq0  13771  znleval2  14153  cncfmptc  14775  cnplimclemr  14848