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  23429  bdayfinbndlem1  28447  segletr  36302  cdlemblem  40230  cdleme21  40774  cdleme22b  40778  cdleme40m  40904  cdlemg34  41149  cdlemk5u  41298  cdlemk6u  41299  cdlemk21N  41310  cdlemk20  41311  cdlemk26b-3  41342  cdlemk26-3  41343  cdlemk28-3  41345  cdlemk37  41351  cdlemky  41363  cdlemk11t  41383  cdlemkyyN  41399  dihmeetlem20N  41763  stoweidlem56  46488