Theorem simp3r1 1288

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 1201	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜑)
2	1	3ad2ant3 1141	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 396   ∧ w3a 1092

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 208  df-an 397  df-3an 1094

This theorem is referenced by:  nllyrest  23469  bdayfinbndlem1  28477  segletr  36342  cdlemblem  40285  cdleme21  40829  cdleme22b  40833  cdleme40m  40959  cdlemg34  41204  cdlemk5u  41353  cdlemk6u  41354  cdlemk21N  41365  cdlemk20  41366  cdlemk26b-3  41397  cdlemk26-3  41398  cdlemk28-3  41400  cdlemk37  41406  cdlemky  41418  cdlemk11t  41438  cdlemkyyN  41454  dihmeetlem20N  41818  stoweidlem56  46499