Theorem simp2l3 1374

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

Assertion

Ref	Expression
simp2l3	⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜂) → 𝜒)

Proof of Theorem simp2l3

Step	Hyp	Ref	Expression
1		simpl3 1247	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜒)
2	1	3ad2ant2 1165	1 ⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜂) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 385   ∧ w3a 1108

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 199  df-an 386  df-3an 1110

This theorem is referenced by:  btwnconn1lem8  32706  btwnconn1lem12  32710  2lplnja  35632  cdlemk21-2N  36904  cdlemk19xlem  36955  jm2.27  38348