Theorem simplr2 1064

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 1028	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜓)
2	1	adantr 276	1 ⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜏) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 104   ∧ w3a 1002

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 1004

This theorem is referenced by:  prarloclemlt  7668  prarloclemlo  7669  seq3f1oleml  10725  ccatswrd  11188  resqrexlemdecn  11509  pcdvdstr  12836  ennnfoneleminc  12968  prdssgrpd  13434  prdsmndd  13467  grprcan  13556  mulgnn0dir  13675  lmodprop2d  14297  lssintclm  14333  psrbaglesuppg  14621  restopnb  14840  cnptopresti  14897  blsscls2  15152