Theorem simplr2 1066

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 1030	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜓)
2	1	adantr 276	1 ⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜏) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 104   ∧ w3a 1004

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 1006

This theorem is referenced by:  prarloclemlt  7713  prarloclemlo  7714  seq3f1oleml  10779  ccatswrd  11255  resqrexlemdecn  11577  pcdvdstr  12905  ennnfoneleminc  13037  prdssgrpd  13503  prdsmndd  13536  grprcan  13625  mulgnn0dir  13744  lmodprop2d  14368  lssintclm  14404  psrbaglesuppg  14692  restopnb  14911  cnptopresti  14968  blsscls2  15223