Theorem simp2l1 1270

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

Assertion

Ref	Expression
simp2l1	⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜂) → 𝜑)

Proof of Theorem simp2l1

Step	Hyp	Ref	Expression
1		simpl1 1189	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜑)
2	1	3ad2ant2 1132	1 ⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜂) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 395   ∧ w3a 1085

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 206  df-an 396  df-3an 1087

This theorem is referenced by:  btwnconn1lem8  34323  btwnconn1lem11  34326  btwnconn1lem12  34327  2lplnja  37560  cdlemk21-2N  38832  cdlemk19xlem  38883  jm2.27  40746