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  10905  ccatswrd  11390  resqrexlemdecn  11725  pcdvdstr  13053  ennnfoneleminc  13249  grprcan  13795  mulgnn0dir  13908  prdssgrpd  14136  prdsmndd  14139  lmodprop2d  14625  lssintclm  14661  psrbaglesuppg  14950  restopnb  15175  cnptopresti  15232  blsscls2  15487