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)

This proof depends on syntax axioms:   → wi 4   ∧ wa 401   ∧ w3a 1103

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402  df-3an 1105

This theorem is used by:  nllyrest  23805  bdayfinbndlem1  28853  segletr  36879  cdlemblem  40850  cdleme21  41394  cdleme22b  41398  cdleme40m  41524  cdlemg34  41769  cdlemk5u  41918  cdlemk6u  41919  cdlemk21N  41930  cdlemk20  41931  cdlemk26b-3  41962  cdlemk26-3  41963  cdlemk28-3  41965  cdlemk37  41971  cdlemky  41983  cdlemk11t  42003  cdlemkyyN  42019  dihmeetlem20N  42383  stoweidlem56  47065