Theorem fimassd 6679

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 6678	. 2 ⊢ (𝐹:𝐴⟶𝐵 → (𝐹 “ 𝑋) ⊆ 𝐵)
3	1, 2	syl 17	1 ⊢ (𝜑 → (𝐹 “ 𝑋) ⊆ 𝐵)

Syntax hints:   → wi 4   ⊆ wss 3898   “ cima 5624  ⟶wf 6484

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2115  ax-9 2123  ax-ext 2705  ax-sep 5238  ax-nul 5248  ax-pr 5374

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1544  df-fal 1554  df-ex 1781  df-sb 2068  df-clab 2712  df-cleq 2725  df-clel 2808  df-ral 3049  df-rex 3058  df-rab 3397  df-v 3439  df-dif 3901  df-un 3903  df-in 3905  df-ss 3915  df-nul 4283  df-if 4477  df-sn 4578  df-pr 4580  df-op 4584  df-br 5096  df-opab 5158  df-xp 5627  df-cnv 5629  df-dm 5631  df-rn 5632  df-res 5633  df-ima 5634  df-f 6492

This theorem is referenced by:  rprmdvdsprod  33508  vonf1owev  35175  weiunfrlem  36531  weiunfr  36534  imo72b2lem0  44285  limsupval3  45817  limsupmnflem  45845  liminfval5  45890  sge0f1o  46507  grimuhgr  48014  uhgrimisgrgric  48058  isubgr3stgrlem6  48098  imasubc  49279  imassc  49281