Theorem simplr2 1071

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

Assertion

Ref	Expression
simplr2	⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜏) → 𝜓)

Proof of Theorem simplr2

Step	Hyp	Ref	Expression
1		simpr2 1035	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜓)
2	1	adantr 276	1 ⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜏) → 𝜓)

This proof depends on syntax axioms:   → wi 4   ∧ wa 104   ∧ w3a 1009

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117  df-3an 1011

This theorem is used by:  prarloclemlt  7860  prarloclemlo  7861  seq3f1oleml  10955  ccatswrd  11444  resqrexlemdecn  11780  pcdvdstr  13108  ennnfoneleminc  13304  grprcan  13844  mulgnn0dir  13957  prdssgrpd  14193  prdsmndd  14196  lmodprop2d  14687  lssintclm  14723  psrbaglesuppg  15059  restopnb  15284  cnptopresti  15341  blsscls2  15596