Theorem simp3r1 1281

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 1194	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜑)
2	1	3ad2ant3 1135	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 395   ∧ w3a 1086

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 1088

This theorem is referenced by:  nllyrest  23495  segletr  36116  cdlemblem  39796  cdleme21  40340  cdleme22b  40344  cdleme40m  40470  cdlemg34  40715  cdlemk5u  40864  cdlemk6u  40865  cdlemk21N  40876  cdlemk20  40877  cdlemk26b-3  40908  cdlemk26-3  40909  cdlemk28-3  40911  cdlemk37  40917  cdlemky  40929  cdlemk11t  40949  cdlemkyyN  40965  dihmeetlem20N  41329  stoweidlem56  46076