Theorem simp3r1 1298

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 1211	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜑)
2	1	3ad2ant3 1151	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 400   ∧ w3a 1101

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 401  df-3an 1103

This theorem is referenced by:  nllyrest  23611  bdayfinbndlem1  28625  segletr  36504  cdlemblem  40456  cdleme21  41000  cdleme22b  41004  cdleme40m  41130  cdlemg34  41375  cdlemk5u  41524  cdlemk6u  41525  cdlemk21N  41536  cdlemk20  41537  cdlemk26b-3  41568  cdlemk26-3  41569  cdlemk28-3  41571  cdlemk37  41577  cdlemky  41589  cdlemk11t  41609  cdlemkyyN  41625  dihmeetlem20N  41989  stoweidlem56  46661