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Theorem imass2d 40280
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 5742 . 2 (𝐴𝐵 → (𝐶𝐴) ⊆ (𝐶𝐵))
31, 2syl 17 1 (𝜑 → (𝐶𝐴) ⊆ (𝐶𝐵))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wss 3798  cima 5345
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1896  ax-4 1910  ax-5 2011  ax-6 2077  ax-7 2114  ax-9 2175  ax-10 2194  ax-11 2209  ax-12 2222  ax-13 2391  ax-ext 2803
This theorem depends on definitions:  df-bi 199  df-an 387  df-or 881  df-3an 1115  df-tru 1662  df-ex 1881  df-nf 1885  df-sb 2070  df-clab 2812  df-cleq 2818  df-clel 2821  df-nfc 2958  df-rab 3126  df-v 3416  df-dif 3801  df-un 3803  df-in 3805  df-ss 3812  df-nul 4145  df-if 4307  df-sn 4398  df-pr 4400  df-op 4404  df-br 4874  df-opab 4936  df-xp 5348  df-cnv 5350  df-dm 5352  df-rn 5353  df-res 5354  df-ima 5355
This theorem is referenced by:  liminflelimsuplem  40802
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