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Theorem simpr21 1262
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 24-Jun-2022.)
Assertion
Ref Expression
simpr21 ((𝜂 ∧ (𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏)) → 𝜑)

Proof of Theorem simpr21
StepHypRef Expression
1 simpr1 1196 . 2 ((𝜂 ∧ (𝜑𝜓𝜒)) → 𝜑)
213ad2antr2 1191 1 ((𝜂 ∧ (𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏)) → 𝜑)
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  33538  cgr3tr4  34096  cdleme27a  38123
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