Theorem fimassd 6732

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 6731	. 2 ⊢ (𝐹:𝐴⟶𝐵 → (𝐹 “ 𝑋) ⊆ 𝐵)
3	1, 2	syl 17	1 ⊢ (𝜑 → (𝐹 “ 𝑋) ⊆ 𝐵)

Syntax hints:   → wi 4   ⊆ wss 3931   “ cima 5662  ⟶wf 6532

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2708  ax-sep 5271  ax-nul 5281  ax-pr 5407

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2066  df-clab 2715  df-cleq 2728  df-clel 2810  df-ral 3053  df-rex 3062  df-rab 3421  df-v 3466  df-dif 3934  df-un 3936  df-in 3938  df-ss 3948  df-nul 4314  df-if 4506  df-sn 4607  df-pr 4609  df-op 4613  df-br 5125  df-opab 5187  df-xp 5665  df-cnv 5667  df-dm 5669  df-rn 5670  df-res 5671  df-ima 5672  df-f 6540

This theorem is referenced by:  rprmdvdsprod  33554  weiunfrlem  36487  weiunfr  36490  imo72b2lem0  44164  limsupval3  45701  limsupmnflem  45729  liminfval5  45774  sge0f1o  46391  grimuhgr  47880  uhgrimisgrgric  47924  isubgr3stgrlem6  47963  imasubc  49071  imassc  49073