Theorem simplr2 1043

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 1007	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜓)
2	1	adantr 276	1 ⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜏) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 104   ∧ w3a 981

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 983

This theorem is referenced by:  prarloclemlt  7613  prarloclemlo  7614  seq3f1oleml  10668  ccatswrd  11131  resqrexlemdecn  11367  pcdvdstr  12694  ennnfoneleminc  12826  prdssgrpd  13291  prdsmndd  13324  grprcan  13413  mulgnn0dir  13532  lmodprop2d  14154  lssintclm  14190  psrbaglesuppg  14478  restopnb  14697  cnptopresti  14754  blsscls2  15009