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 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  23515  segletr  36078  cdlemblem  39750  cdleme21  40294  cdleme22b  40298  cdleme40m  40424  cdlemg34  40669  cdlemk5u  40818  cdlemk6u  40819  cdlemk21N  40830  cdlemk20  40831  cdlemk26b-3  40862  cdlemk26-3  40863  cdlemk28-3  40865  cdlemk37  40871  cdlemky  40883  cdlemk11t  40903  cdlemkyyN  40919  dihmeetlem20N  41283  stoweidlem56  45977