Theorem 3simpc 1022

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 1009	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) ↔ (𝜓 ∧ 𝜒 ∧ 𝜑))
2		3simpa 1020	. 2 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜑) → (𝜓 ∧ 𝜒))
3	1, 2	sylbi 121	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → (𝜓 ∧ 𝜒))

Syntax hints:   → wi 4   ∧ wa 104   ∧ w3a 1004

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 1006

This theorem is referenced by:  simp3  1025  3adant1  1041  3adantl1  1179  3adantr1  1182  eupickb  2161  find  4697  fovcld  6126  fisseneq  7127  eqsupti  7195  divcanap2  8860  diveqap0  8862  divrecap  8868  divcanap3  8878  eliooord  10163  fzrev3  10322  sqdivap  10866  swrdlend  11240  swrdnd  11241  ccats1pfxeqbi  11324  muldvds2  12380  dvdscmul  12381  dvdsmulc  12382  dvdstr  12391  domneq0  14289  znleval2  14671  cncfmptc  15323  cnplimclemr  15396  uhgr2edg  16060  umgr2edgneu  16066  clwwlknp  16271