Theorem simpll2 984

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Assertion

Ref	Expression
simpll2	⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) → 𝜓)

Proof of Theorem simpll2

Step	Hyp	Ref	Expression
1		simpl2 948	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜓)
2	1	adantr 271	1 ⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 103   ∧ w3a 925

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106

This theorem depends on definitions:  df-bi 116  df-3an 927

This theorem is referenced by:  fidceq  6639  fidifsnen  6640  en2eqpr  6677  iunfidisj  6709  cauappcvgprlemlol  7267  caucvgprlemlol  7290  caucvgprprlemlol  7318  elfzonelfzo  9702  qbtwnre  9729  hashun  10274  subcn2  10761  divalglemex  11261  divalglemeuneg  11262  dvdslegcd  11295  lcmledvds  11391