Theorem simp3r1 1282

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 1195	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜑)
2	1	3ad2ant3 1135	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 395   ∧ 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 207  df-an 396  df-3an 1088

This theorem is referenced by:  nllyrest  23429  segletr  36137  cdlemblem  39817  cdleme21  40361  cdleme22b  40365  cdleme40m  40491  cdlemg34  40736  cdlemk5u  40885  cdlemk6u  40886  cdlemk21N  40897  cdlemk20  40898  cdlemk26b-3  40929  cdlemk26-3  40930  cdlemk28-3  40932  cdlemk37  40938  cdlemky  40950  cdlemk11t  40970  cdlemkyyN  40986  dihmeetlem20N  41350  stoweidlem56  46065