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 1133	1 ⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) ∧ 𝜂 ∧ 𝜁) → 𝜒)

Syntax hints:   → wi 4   ∧ w3a 1086

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 1088

This theorem is referenced by:  ax5seglem3  29004  axpasch  29014  exatleN  39664  ps-2b  39742  3atlem1  39743  3atlem2  39744  3atlem4  39746  3atlem5  39747  3atlem6  39748  2llnjaN  39826  2llnjN  39827  4atlem12b  39871  2lplnja  39879  2lplnj  39880  dalemrea  39888  dath2  39997  lneq2at  40038  osumcllem7N  40222  cdleme26ee  40620  cdlemg35  40973  cdlemg36  40974  cdlemj1  41081  cdlemk23-3  41162  cdlemk25-3  41164  cdlemk26b-3  41165  cdlemk27-3  41167  cdlemk28-3  41168  cdleml3N  41238  iscnrm3llem2  49195