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Theorem simpr11 1143
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simpr11 ((𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏)) → 𝜑)

Proof of Theorem simpr11
StepHypRef Expression
1 simp11 1089 . 2 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜑)
21adantl 482 1 ((𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏)) → 𝜑)
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  15820  cgr3tr4  31798  btwnoutside  31871  paddasslem8  34590  cdleme27a  35132
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