Theorem simplr3 1065

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 1029	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜒)
2	1	adantr 276	1 ⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜏) → 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:  netap  7448  prarloclemlt  7688  prarloclemlo  7689  ccatswrd  11210  pfxccat3  11274  resqrexlemdecn  11531  summodclem2  11901  isumss2  11912  pcdvdstr  12858  ennnfoneleminc  12990  prdssgrpd  13456  prdsmndd  13489  grprcan  13578  mulgnn0dir  13697  mulgdir  13699  mulgass  13704  lmodprop2d  14320  lssintclm  14356  psrbaglesuppg  14644  restopnb  14863  blsscls2  15175