Theorem simp1r1 1270

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

Assertion

Ref	Expression
simp1r1	⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜏 ∧ 𝜂) → 𝜑)

Proof of Theorem simp1r1

Step	Hyp	Ref	Expression
1		simpr1 1195	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜑)
2	1	3ad2ant1 1134	1 ⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜏 ∧ 𝜂) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 399   ∧ w3a 1088

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 210  df-an 400  df-3an 1090

This theorem is referenced by:  trisegint  33960  lshpkrlem6  36741  atbtwnexOLDN  37073  atbtwnex  37074  3dim3  37095  3atlem5  37113  4atlem11  37235  4atexlem7  37701  cdleme22b  37967