Theorem simp123 1308

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 1209	. 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  28946  axpasch  28956  exatleN  39406  ps-2b  39484  3atlem1  39485  3atlem2  39486  3atlem4  39488  3atlem5  39489  3atlem6  39490  2llnjaN  39568  2llnjN  39569  4atlem12b  39613  2lplnja  39621  2lplnj  39622  dalemrea  39630  dath2  39739  lneq2at  39780  osumcllem7N  39964  cdleme26ee  40362  cdlemg35  40715  cdlemg36  40716  cdlemj1  40823  cdlemk23-3  40904  cdlemk25-3  40906  cdlemk26b-3  40907  cdlemk27-3  40909  cdlemk28-3  40910  cdleml3N  40980  iscnrm3llem2  48847