Theorem simp121 1306

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

Assertion

Ref	Expression
simp121	⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) ∧ 𝜂 ∧ 𝜁) → 𝜑)

Proof of Theorem simp121

Step	Hyp	Ref	Expression
1		simp21 1207	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜑)
2	1	3ad2ant1 1133	1 ⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) ∧ 𝜂 ∧ 𝜁) → 𝜑)

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  28858  axpasch  28868  exatleN  39398  ps-2b  39476  3atlem1  39477  3atlem2  39478  3atlem4  39480  3atlem5  39481  3atlem6  39482  2llnjaN  39560  4atlem12b  39605  2lplnja  39613  dalempea  39620  dath2  39731  lneq2at  39772  llnexchb2  39863  dalawlem1  39865  osumcllem7N  39956  lhpexle3lem  40005  cdleme26ee  40354  cdlemg34  40706  cdlemg36  40708  cdlemj1  40815  cdlemj2  40816  cdlemk23-3  40896  cdlemk25-3  40898  cdlemk26b-3  40899  cdlemk26-3  40900  cdlemk27-3  40901  cdleml3N  40972  iscnrm3llem2  48938