Theorem simp3r3 1282

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

Assertion

Ref	Expression
simp3r3	⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜒)

Proof of Theorem simp3r3

Step	Hyp	Ref	Expression
1		simpr3 1195	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜒)
2	1	3ad2ant3 1134	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 396   ∧ w3a 1086

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 397  df-3an 1088

This theorem is referenced by:  nllyrest  22637  cdlemblem  37807  cdleme21  38351  cdleme22b  38355  cdleme40m  38481  cdlemg34  38726  cdlemk5u  38875  cdlemk6u  38876  cdlemk21N  38887  cdlemk20  38888  cdlemk26b-3  38919  cdlemk26-3  38920  cdlemk28-3  38922  cdlemky  38940  cdlemk11t  38960  cdlemkyyN  38976  dihmeetlem20N  39340  stoweidlem56  43597