Theorem simplr2 1071

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 1035	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜓)
2	1	adantr 276	1 ⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜏) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 104   ∧ w3a 1009

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 1011

This theorem is referenced by:  prarloclemlt  7854  prarloclemlo  7855  seq3f1oleml  10936  ccatswrd  11425  resqrexlemdecn  11761  pcdvdstr  13089  ennnfoneleminc  13285  grprcan  13825  mulgnn0dir  13938  prdssgrpd  14174  prdsmndd  14177  lmodprop2d  14668  lssintclm  14704  psrbaglesuppg  15040  restopnb  15265  cnptopresti  15322  blsscls2  15577