Theorem ssct 9024

Description: Any subset of a countable set is countable. (Contributed by Thierry Arnoux, 31-Jan-2017.) Avoid ax-pow 5319, ax-un 7713. (Revised by BTernaryTau, 7-Dec-2024.)

Assertion

Ref	Expression
ssct	⊢ ((𝐴 ⊆ 𝐵 ∧ 𝐵 ≼ ω) → 𝐴 ≼ ω)

Proof of Theorem ssct

Step	Hyp	Ref	Expression
1		domssl 8973	1 ⊢ ((𝐴 ⊆ 𝐵 ∧ 𝐵 ≼ ω) → 𝐴 ≼ ω)

Syntax hints:   → wi 4   ∧ wa 399   ⊆ wss 3902   class class class wbr 5097  ωcom 7841   ≼ cdom 8919

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1814  ax-4 1828  ax-5 1929  ax-6 1986  ax-7 2027  ax-8 2143  ax-9 2151  ax-ext 2733  ax-sep 5243  ax-pr 5387

This theorem depends on definitions:  df-bi 209  df-an 400  df-or 859  df-3an 1099  df-tru 1562  df-fal 1572  df-ex 1799  df-sb 2090  df-clab 2740  df-cleq 2753  df-clel 2836  df-ral 3076  df-rex 3086  df-rab 3414  df-v 3455  df-dif 3905  df-un 3907  df-in 3909  df-ss 3919  df-nul 4284  df-if 4478  df-sn 4580  df-pr 4582  df-op 4586  df-br 5098  df-opab 5160  df-xp 5649  df-rel 5650  df-cnv 5651  df-co 5652  df-dm 5653  df-rn 5654  df-res 5655  df-fun 6518  df-fn 6519  df-f 6520  df-f1 6521  df-dom 8923

This theorem is referenced by:  measvuni  34472  measiuns  34475  sxbrsigalem1  34543  ssnct  45618  fzct  45915  fzoct  45920  salexct  46869  opnvonmbllem2  47168