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Theorem simp112 1388
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp112 ((((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜂𝜁) → 𝜓)

Proof of Theorem simp112
StepHypRef Expression
1 simp12 1247 . 2 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜓)
213ad2ant1 1128 1 ((((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜂𝜁) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1072
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 197  df-an 385  df-3an 1074
This theorem is referenced by:  axcontlem4  26067  ps-2b  35289  llncvrlpln2  35364  4atlem11b  35415  4atlem12b  35418  2lnat  35591  cdlemblem  35600  4atexlemex6  35881  cdleme24  36160  cdleme26ee  36168  cdlemg2idN  36404  cdlemg31c  36507  cdlemk26-3  36714  dihglblem2N  37103  0ellimcdiv  40402
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