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Theorem simpr13 1254
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 1191 . 2 ((𝜂 ∧ (𝜑𝜓𝜒)) → 𝜒)
213ad2antr1 1183 1 ((𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏)) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 398  w3a 1082
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 209  df-an 399  df-3an 1084
This theorem is referenced by:  cgr3tr4  33506  btwnoutside  33579  paddasslem8  36955  cdleme27a  37495  itsclc0yqe  44738
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