Theorem fimassd 43149

Description: The image of a class is a subset of its codomain. (Contributed by Glauco Siliprandi, 23-Oct-2021.)

Hypothesis

Ref	Expression
fimassd.1	⊢ (𝜑 → 𝐹:𝐴⟶𝐵)

Assertion

Ref	Expression
fimassd	⊢ (𝜑 → (𝐹 “ 𝑋) ⊆ 𝐵)

Proof of Theorem fimassd

Step	Hyp	Ref	Expression
1		fimassd.1	. 2 ⊢ (𝜑 → 𝐹:𝐴⟶𝐵)
2		fimass 6677	. 2 ⊢ (𝐹:𝐴⟶𝐵 → (𝐹 “ 𝑋) ⊆ 𝐵)
3	1, 2	syl 17	1 ⊢ (𝜑 → (𝐹 “ 𝑋) ⊆ 𝐵)

Syntax hints:   → wi 4   ⊆ wss 3902   “ cima 5628  ⟶wf 6480

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2708  ax-sep 5248  ax-nul 5255  ax-pr 5377

This theorem depends on definitions:  df-bi 206  df-an 398  df-or 846  df-3an 1089  df-tru 1544  df-fal 1554  df-ex 1782  df-sb 2068  df-clab 2715  df-cleq 2729  df-clel 2815  df-ral 3063  df-rex 3072  df-rab 3405  df-v 3444  df-dif 3905  df-un 3907  df-in 3909  df-ss 3919  df-nul 4275  df-if 4479  df-sn 4579  df-pr 4581  df-op 4585  df-br 5098  df-opab 5160  df-xp 5631  df-cnv 5633  df-dm 5635  df-rn 5636  df-res 5637  df-ima 5638  df-f 6488

This theorem is referenced by:  limsupval3  43619  limsupmnflem  43647  liminfval5  43692