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Theorem simpr13 1261
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 24-Jun-2022.)
Assertion
Ref Expression
simpr13 ((𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏)) → 𝜒)

Proof of Theorem simpr13
StepHypRef Expression
1 simpr3 1198 . 2 ((𝜂 ∧ (𝜑𝜓𝜒)) → 𝜒)
213ad2antr1 1190 1 ((𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏)) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 399  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:  poxp3  33559  cgr3tr4  34117  btwnoutside  34190  paddasslem8  37604  cdleme27a  38144  itsclc0yqe  45808
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