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  10974  ccatswrd  11464  resqrexlemdecn  11800  pcdvdstr  13135  ennnfoneleminc  13360  grprcan  13901  mulgnn0dir  14014  prdssgrpd  14298  prdsmndd  14301  lmodprop2d  14794  lssintclm  14830  psrbaglesuppg  15171  mplsubgfilemcl  15246  restopnb  15440  cnptopresti  15497  blsscls2  15752