Theorem simplr1 1041

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

Assertion

Ref	Expression
simplr1	⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜏) → 𝜑)

Proof of Theorem simplr1

Step	Hyp	Ref	Expression
1		simpr1 1005	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜑)
2	1	adantr 276	1 ⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜏) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 104   ∧ w3a 980

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 982

This theorem is referenced by:  netap  7339  prarloclemlt  7579  prarloclemlo  7580  summodclem2  11566  pcdvdstr  12523  prdssgrpd  13119  prdsmndd  13152  grprcan  13241  lmodprop2d  13982  lssintclm  14018  psrbaglesuppg  14306  restopnb  14525  blsscls2  14837