Theorem simp3r1 1279

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 1192	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜑)
2	1	3ad2ant3 1133	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 395   ∧ w3a 1085

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 206  df-an 396  df-3an 1087

This theorem is referenced by:  nllyrest  22545  segletr  34343  cdlemblem  37734  cdleme21  38278  cdleme22b  38282  cdleme40m  38408  cdlemg34  38653  cdlemk5u  38802  cdlemk6u  38803  cdlemk21N  38814  cdlemk20  38815  cdlemk26b-3  38846  cdlemk26-3  38847  cdlemk28-3  38849  cdlemk37  38855  cdlemky  38867  cdlemk11t  38887  cdlemkyyN  38903  dihmeetlem20N  39267  stoweidlem56  43487