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Theorem imass2d 44667
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 6111 . 2 (𝐴𝐵 → (𝐶𝐴) ⊆ (𝐶𝐵))
31, 2syl 17 1 (𝜑 → (𝐶𝐴) ⊆ (𝐶𝐵))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wss 3949  cima 5685
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2699
This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2706  df-cleq 2720  df-clel 2806  df-rab 3431  df-v 3475  df-dif 3952  df-un 3954  df-in 3956  df-ss 3966  df-nul 4327  df-if 4533  df-sn 4633  df-pr 4635  df-op 4639  df-br 5153  df-opab 5215  df-xp 5688  df-cnv 5690  df-dm 5692  df-rn 5693  df-res 5694  df-ima 5695
This theorem is referenced by:  liminflelimsuplem  45192
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