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  7867  prarloclemlo  7868  seq3f1oleml  10975  ccatswrd  11465  resqrexlemdecn  11801  pcdvdstr  13136  ennnfoneleminc  13361  grprcan  13902  mulgnn0dir  14015  prdssgrpd  14299  prdsmndd  14302  lmodprop2d  14795  lssintclm  14831  psrbaglesuppg  15172  restopnb  15419  cnptopresti  15476  blsscls2  15731