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Theorem imass2d 45207
Description: Subset theorem for image. (Contributed by Glauco Siliprandi, 2-Jan-2022.)
Hypothesis
Ref Expression
imass2d.1 (𝜑𝐴𝐵)
Assertion
Ref Expression
imass2d (𝜑 → (𝐶𝐴) ⊆ (𝐶𝐵))

Proof of Theorem imass2d
StepHypRef Expression
1 imass2d.1 . 2 (𝜑𝐴𝐵)
2 imass2 6123 . 2 (𝐴𝐵 → (𝐶𝐴) ⊆ (𝐶𝐵))
31, 2syl 17 1 (𝜑 → (𝐶𝐴) ⊆ (𝐶𝐵))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wss 3963  cima 5692
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1540  df-fal 1550  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-rab 3434  df-v 3480  df-dif 3966  df-un 3968  df-in 3970  df-ss 3980  df-nul 4340  df-if 4532  df-sn 4632  df-pr 4634  df-op 4638  df-br 5149  df-opab 5211  df-xp 5695  df-cnv 5697  df-dm 5699  df-rn 5700  df-res 5701  df-ima 5702
This theorem is referenced by:  liminflelimsuplem  45731
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