Theorem simplr3 1068

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Assertion

Ref	Expression
simplr3	⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜏) → 𝜒)

Proof of Theorem simplr3

Step	Hyp	Ref	Expression
1		simpr3 1032	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜒)
2	1	adantr 276	1 ⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜏) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 104   ∧ w3a 1005

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 1007

This theorem is referenced by:  netap  7584  prarloclemlt  7824  prarloclemlo  7825  ccatswrd  11390  pfxccat3  11454  resqrexlemdecn  11725  summodclem2  12096  isumss2  12107  pcdvdstr  13053  ennnfoneleminc  13249  grprcan  13795  mulgnn0dir  13908  mulgdir  13910  mulgass  13915  prdssgrpd  14136  prdsmndd  14139  lmodprop2d  14625  lssintclm  14661  psrbaglesuppg  14950  restopnb  15175  blsscls2  15487