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Theorem simp133 1312
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp133 (((𝜃𝜏 ∧ (𝜑𝜓𝜒)) ∧ 𝜂𝜁) → 𝜒)

Proof of Theorem simp133
StepHypRef Expression
1 simp33 1213 . 2 ((𝜃𝜏 ∧ (𝜑𝜓𝜒)) → 𝜒)
213ad2ant1 1135 1 (((𝜃𝜏 ∧ (𝜑𝜓𝜒)) ∧ 𝜂𝜁) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1089
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 210  df-an 400  df-3an 1091
This theorem is referenced by:  tsmsxp  23065  ax5seglem3  27035  exatleN  37168  3atlem1  37247  3atlem2  37248  3atlem6  37252  4atlem11b  37372  4atlem12b  37375  lplncvrlvol2  37379  dalemuea  37395  dath2  37501  4atexlemex6  37838  cdleme22f2  38111  cdleme22g  38112  cdlemg7aN  38389  cdlemg31c  38463  cdlemg36  38478  cdlemj1  38585  cdlemj2  38586  cdlemk23-3  38666  cdlemk26b-3  38669
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