Theorem simp3r1 1278

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 1191	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜑)
2	1	3ad2ant3 1132	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 394   ∧ w3a 1084

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 395  df-3an 1086

This theorem is referenced by:  nllyrest  23408  segletr  35715  cdlemblem  39270  cdleme21  39814  cdleme22b  39818  cdleme40m  39944  cdlemg34  40189  cdlemk5u  40338  cdlemk6u  40339  cdlemk21N  40350  cdlemk20  40351  cdlemk26b-3  40382  cdlemk26-3  40383  cdlemk28-3  40385  cdlemk37  40391  cdlemky  40403  cdlemk11t  40423  cdlemkyyN  40439  dihmeetlem20N  40803  stoweidlem56  45446