Theorem simp123 1309

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

Assertion

Ref	Expression
simp123	⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) ∧ 𝜂 ∧ 𝜁) → 𝜒)

Proof of Theorem simp123

Step	Hyp	Ref	Expression
1		simp23 1210	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜒)
2	1	3ad2ant1 1134	1 ⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) ∧ 𝜂 ∧ 𝜁) → 𝜒)

Syntax hints:   → wi 4   ∧ 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:  ax5seglem3  29016  axpasch  29026  exatleN  39777  ps-2b  39855  3atlem1  39856  3atlem2  39857  3atlem4  39859  3atlem5  39860  3atlem6  39861  2llnjaN  39939  2llnjN  39940  4atlem12b  39984  2lplnja  39992  2lplnj  39993  dalemrea  40001  dath2  40110  lneq2at  40151  osumcllem7N  40335  cdleme26ee  40733  cdlemg35  41086  cdlemg36  41087  cdlemj1  41194  cdlemk23-3  41275  cdlemk25-3  41277  cdlemk26b-3  41278  cdlemk27-3  41280  cdlemk28-3  41281  cdleml3N  41351  iscnrm3llem2  49306