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Theorem simpr3r 1234
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 24-Jun-2022.)
Assertion
Ref Expression
simpr3r ((𝜏 ∧ (𝜒𝜃 ∧ (𝜑𝜓))) → 𝜓)

Proof of Theorem simpr3r
StepHypRef Expression
1 simprr 773 . 2 ((𝜏 ∧ (𝜑𝜓)) → 𝜓)
213ad2antr3 1189 1 ((𝜏 ∧ (𝜒𝜃 ∧ (𝜑𝜓))) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 395  w3a 1086
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 207  df-an 396  df-3an 1088
This theorem is referenced by:  poxp2  8167  ax5seg  28968  segconeq  35992  ifscgr  36026  btwnconn1lem9  36077  btwnconn1lem11  36079  btwnconn1lem12  36080  lplnexllnN  39547  cdleme3b  40212  cdleme3c  40213  cdleme3e  40215  cdleme27a  40350
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