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)

Syntax hints:   → wi 4   ∧ wa 400   ∧ w3a 1103

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 1105

This theorem is referenced by:  nllyrest  23643  bdayfinbndlem1  28660  segletr  36606  cdlemblem  40567  cdleme21  41111  cdleme22b  41115  cdleme40m  41241  cdlemg34  41486  cdlemk5u  41635  cdlemk6u  41636  cdlemk21N  41647  cdlemk20  41648  cdlemk26b-3  41679  cdlemk26-3  41680  cdlemk28-3  41682  cdlemk37  41688  cdlemky  41700  cdlemk11t  41720  cdlemkyyN  41736  dihmeetlem20N  42100  stoweidlem56  46770