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Theorem simpr11 1332
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 24-Jun-2022.)
Assertion
Ref Expression
simpr11 ((𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏)) → 𝜑)

Proof of Theorem simpr11
StepHypRef Expression
1 simpr1 1233 . 2 ((𝜂 ∧ (𝜑𝜓𝜒)) → 𝜑)
213ad2antr1 1203 1 ((𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏)) → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382  w3a 1071
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 383  df-3an 1073
This theorem is referenced by:  setsstructOLD  16106  clwwlknonex2  27285  cgr3tr4  32496  btwnoutside  32569  paddasslem8  35635  cdleme27a  36176
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