Theorem simp3r1 1283

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

Assertion

Ref	Expression
simp3r1	⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜑)

Proof of Theorem simp3r1

Step	Hyp	Ref	Expression
1		simpr1 1196	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜑)
2	1	3ad2ant3 1137	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 399   ∧ w3a 1089

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 1091

This theorem is referenced by:  nllyrest  22337  segletr  34102  cdlemblem  37493  cdleme21  38037  cdleme22b  38041  cdleme40m  38167  cdlemg34  38412  cdlemk5u  38561  cdlemk6u  38562  cdlemk21N  38573  cdlemk20  38574  cdlemk26b-3  38605  cdlemk26-3  38606  cdlemk28-3  38608  cdlemk37  38614  cdlemky  38626  cdlemk11t  38646  cdlemkyyN  38662  dihmeetlem20N  39026  stoweidlem56  43215