Theorem simplr3 1044

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 1008	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜒)
2	1	adantr 276	1 ⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜏) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 104   ∧ w3a 981

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 983

This theorem is referenced by:  netap  7373  prarloclemlt  7613  prarloclemlo  7614  ccatswrd  11131  resqrexlemdecn  11367  summodclem2  11737  isumss2  11748  pcdvdstr  12694  ennnfoneleminc  12826  prdssgrpd  13291  prdsmndd  13324  grprcan  13413  mulgnn0dir  13532  mulgdir  13534  mulgass  13539  lmodprop2d  14154  lssintclm  14190  psrbaglesuppg  14478  restopnb  14697  blsscls2  15009