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 1136	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 395   ∧ w3a 1087

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 1089

This theorem is referenced by:  nllyrest  23442  bdayfinbndlem1  28475  segletr  36330  cdlemblem  40169  cdleme21  40713  cdleme22b  40717  cdleme40m  40843  cdlemg34  41088  cdlemk5u  41237  cdlemk6u  41238  cdlemk21N  41249  cdlemk20  41250  cdlemk26b-3  41281  cdlemk26-3  41282  cdlemk28-3  41284  cdlemk37  41290  cdlemky  41302  cdlemk11t  41322  cdlemkyyN  41338  dihmeetlem20N  41702  stoweidlem56  46414