Theorem simp3r3 1290

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Assertion

Ref	Expression
simp3r3	⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜒)

Proof of Theorem simp3r3

Step	Hyp	Ref	Expression
1		simpr3 1203	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜒)
2	1	3ad2ant3 1141	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 396   ∧ w3a 1092

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 208  df-an 397  df-3an 1094

This theorem is referenced by:  hash7g  14446  nllyrest  23476  bdayfinbndlem1  28484  cdlemblem  40292  cdleme21  40836  cdleme22b  40840  cdleme40m  40966  cdlemg34  41211  cdlemk5u  41360  cdlemk6u  41361  cdlemk21N  41372  cdlemk20  41373  cdlemk26b-3  41404  cdlemk26-3  41405  cdlemk28-3  41407  cdlemky  41425  cdlemk11t  41445  cdlemkyyN  41461  dihmeetlem20N  41825  stoweidlem56  46506