Theorem fimassd 6758

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 6757	. 2 ⊢ (𝐹:𝐴⟶𝐵 → (𝐹 “ 𝑋) ⊆ 𝐵)
3	1, 2	syl 17	1 ⊢ (𝜑 → (𝐹 “ 𝑋) ⊆ 𝐵)

Syntax hints:   → wi 4   ⊆ wss 3963   “ cima 5692  ⟶wf 6559

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706  ax-sep 5302  ax-nul 5312  ax-pr 5438

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1540  df-fal 1550  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-ral 3060  df-rex 3069  df-rab 3434  df-v 3480  df-dif 3966  df-un 3968  df-in 3970  df-ss 3980  df-nul 4340  df-if 4532  df-sn 4632  df-pr 4634  df-op 4638  df-br 5149  df-opab 5211  df-xp 5695  df-cnv 5697  df-dm 5699  df-rn 5700  df-res 5701  df-ima 5702  df-f 6567

This theorem is referenced by:  rprmdvdsprod  33542  weiunfrlem  36447  weiunfr  36450  imo72b2lem0  44155  limsupval3  45648  limsupmnflem  45676  liminfval5  45721  sge0f1o  46338  grimuhgr  47816  uhgrimisgrgric  47837  isubgr3stgrlem6  47874