Theorem simplr2 1042

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 1006	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜓)
2	1	adantr 276	1 ⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜏) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 104   ∧ w3a 980

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 982

This theorem is referenced by:  prarloclemlt  7579  prarloclemlo  7580  seq3f1oleml  10627  resqrexlemdecn  11196  pcdvdstr  12523  ennnfoneleminc  12655  prdssgrpd  13119  prdsmndd  13152  grprcan  13241  mulgnn0dir  13360  lmodprop2d  13982  lssintclm  14018  psrbaglesuppg  14306  restopnb  14525  cnptopresti  14582  blsscls2  14837