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  7696  prarloclemlo  7697  seq3f1oleml  10755  ccatswrd  11223  resqrexlemdecn  11544  pcdvdstr  12871  ennnfoneleminc  13003  prdssgrpd  13469  prdsmndd  13502  grprcan  13591  mulgnn0dir  13710  lmodprop2d  14333  lssintclm  14369  psrbaglesuppg  14657  restopnb  14876  cnptopresti  14933  blsscls2  15188