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Theorem simpr3r 1301
 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 813 . 2 ((𝜏 ∧ (𝜑𝜓)) → 𝜓)
213ad2antr3 1206 1 ((𝜏 ∧ (𝜒𝜃 ∧ (𝜑𝜓))) → 𝜓)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 383   ∧ w3a 1072 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 197  df-an 385  df-3an 1074 This theorem is referenced by:  ax5seg  26038  segconeq  32444  ifscgr  32478  btwnconn1lem9  32529  btwnconn1lem11  32531  btwnconn1lem12  32532  lplnexllnN  35371  cdleme3b  36037  cdleme3c  36038  cdleme3e  36040  cdleme27a  36175
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