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Theorem simp111 1299
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp111 ((((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜂𝜁) → 𝜑)

Proof of Theorem simp111
StepHypRef Expression
1 simp11 1200 . 2 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜑)
213ad2ant1 1130 1 ((((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜂𝜁) → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1084
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 206  df-an 396  df-3an 1086
This theorem is referenced by:  tsmsxp  24009  ps-2b  38865  llncvrlpln2  38940  4atlem11b  38991  4atlem12b  38994  lplncvrlvol2  38998  lneq2at  39161  2lnat  39167  cdlemblem  39176  4atexlemex6  39457  cdleme24  39735  cdleme26ee  39743  cdlemg2idN  39979  cdlemg31c  40082  cdlemk26-3  40289  0ellimcdiv  44919
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