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  7688  prarloclemlo  7689  seq3f1oleml  10746  ccatswrd  11210  resqrexlemdecn  11531  pcdvdstr  12858  ennnfoneleminc  12990  prdssgrpd  13456  prdsmndd  13489  grprcan  13578  mulgnn0dir  13697  lmodprop2d  14320  lssintclm  14356  psrbaglesuppg  14644  restopnb  14863  cnptopresti  14920  blsscls2  15175