Theorem 3simpc 1020

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 1007	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) ↔ (𝜓 ∧ 𝜒 ∧ 𝜑))
2		3simpa 1018	. 2 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜑) → (𝜓 ∧ 𝜒))
3	1, 2	sylbi 121	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → (𝜓 ∧ 𝜒))

Syntax hints:   → wi 4   ∧ wa 104   ∧ w3a 1002

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 1004

This theorem is referenced by:  simp3  1023  3adant1  1039  3adantl1  1177  3adantr1  1180  eupickb  2159  find  4695  fovcld  6121  fisseneq  7121  eqsupti  7189  divcanap2  8853  diveqap0  8855  divrecap  8861  divcanap3  8871  eliooord  10156  fzrev3  10315  sqdivap  10858  swrdlend  11232  swrdnd  11233  ccats1pfxeqbi  11316  muldvds2  12371  dvdscmul  12372  dvdsmulc  12373  dvdstr  12382  domneq0  14279  znleval2  14661  cncfmptc  15313  cnplimclemr  15386  uhgr2edg  16050  umgr2edgneu  16056  clwwlknp  16226