Theorem simplr2 1067

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 1031	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜓)
2	1	adantr 276	1 ⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜏) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 104   ∧ w3a 1005

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 1007

This theorem is referenced by:  prarloclemlt  7824  prarloclemlo  7825  seq3f1oleml  10902  ccatswrd  11387  resqrexlemdecn  11722  pcdvdstr  13050  ennnfoneleminc  13246  prdssgrpd  13712  prdsmndd  13745  grprcan  13834  mulgnn0dir  13953  lmodprop2d  14608  lssintclm  14644  psrbaglesuppg  14933  restopnb  15158  cnptopresti  15215  blsscls2  15470