Theorem simp3r1 1300

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 1213	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜑)
2	1	3ad2ant3 1153	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜑)

This proof depends on syntax axioms:   → wi 4   ∧ wa 401   ∧ w3a 1103

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402  df-3an 1105

This theorem is used by:  nllyrest  23696  bdayfinbndlem1  28713  segletr  36645  cdlemblem  40627  cdleme21  41171  cdleme22b  41175  cdleme40m  41301  cdlemg34  41546  cdlemk5u  41695  cdlemk6u  41696  cdlemk21N  41707  cdlemk20  41708  cdlemk26b-3  41739  cdlemk26-3  41740  cdlemk28-3  41742  cdlemk37  41748  cdlemky  41760  cdlemk11t  41780  cdlemkyyN  41796  dihmeetlem20N  42160  stoweidlem56  46830