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Theorem eqimssd 40170
Description: Equality implies inclusion, deduction version. (Contributed by SN, 6-Nov-2024.)
Hypothesis
Ref Expression
eqimssd.1 (𝜑𝐴 = 𝐵)
Assertion
Ref Expression
eqimssd (𝜑𝐴𝐵)

Proof of Theorem eqimssd
StepHypRef Expression
1 eqimssd.1 . 2 (𝜑𝐴 = 𝐵)
2 ssid 3944 . 2 𝐵𝐵
31, 2eqsstrdi 3976 1 (𝜑𝐴𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1539  wss 3888
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2709
This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1542  df-ex 1783  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-v 3433  df-in 3895  df-ss 3905
This theorem is referenced by: (None)
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