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Theorem simpr12 1250
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 24-Jun-2022.)
Assertion
Ref Expression
simpr12 ((𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏)) → 𝜓)

Proof of Theorem simpr12
StepHypRef Expression
1 simpr2 1187 . 2 ((𝜂 ∧ (𝜑𝜓𝜒)) → 𝜓)
213ad2antr1 1180 1 ((𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏)) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 396  w3a 1079
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 208  df-an 397  df-3an 1081
This theorem is referenced by:  cgr3tr4  33410  btwnoutside  33483  paddasslem8  36843  cdleme27a  37383  itsclc0yqe  44676
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