Theorem simp3r1 1295

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 1208	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜑)
2	1	3ad2ant3 1148	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 399   ∧ w3a 1098

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 209  df-an 400  df-3an 1100

This theorem is referenced by:  nllyrest  23546  bdayfinbndlem1  28560  segletr  36464  cdlemblem  40417  cdleme21  40961  cdleme22b  40965  cdleme40m  41091  cdlemg34  41336  cdlemk5u  41485  cdlemk6u  41486  cdlemk21N  41497  cdlemk20  41498  cdlemk26b-3  41529  cdlemk26-3  41530  cdlemk28-3  41532  cdlemk37  41538  cdlemky  41550  cdlemk11t  41570  cdlemkyyN  41586  dihmeetlem20N  41950  stoweidlem56  46630