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Theorem simpr12 1144
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simpr12 ((𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏)) → 𝜓)

Proof of Theorem simpr12
StepHypRef Expression
1 simp12 1090 . 2 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜓)
21adantl 482 1 ((𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏)) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384  w3a 1036
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 386  df-3an 1038
This theorem is referenced by:  setsstructOLD  15880  cgr3tr4  32134  btwnoutside  32207  paddasslem8  34932  cdleme27a  35474
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