Theorem fimassd 6683

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 6682	. 2 ⊢ (𝐹:𝐴⟶𝐵 → (𝐹 “ 𝑋) ⊆ 𝐵)
3	1, 2	syl 17	1 ⊢ (𝜑 → (𝐹 “ 𝑋) ⊆ 𝐵)

Syntax hints:   → wi 4   ⊆ wss 3890   “ cima 5628  ⟶wf 6488

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-ext 2712  ax-sep 5225  ax-pr 5369

This theorem depends on definitions:  df-bi 208  df-an 397  df-or 854  df-3an 1094  df-tru 1550  df-fal 1560  df-ex 1787  df-sb 2074  df-clab 2719  df-cleq 2732  df-clel 2815  df-ral 3055  df-rex 3065  df-rab 3393  df-v 3434  df-dif 3893  df-un 3895  df-in 3897  df-ss 3907  df-nul 4269  df-if 4462  df-sn 4563  df-pr 4565  df-op 4569  df-br 5080  df-opab 5142  df-xp 5631  df-cnv 5633  df-dm 5635  df-rn 5636  df-res 5637  df-ima 5638  df-f 6496

This theorem is referenced by:  rprmdvdsprod  33624  vonf1owev  35343  weiunfrlem  36699  weiunfr  36702  imo72b2lem0  44616  limsupval3  46142  limsupmnflem  46170  liminfval5  46215  sge0f1o  46832  grimuhgr  48385  uhgrimisgrgric  48429  isubgr3stgrlem6  48469  imasubc  49648  imassc  49650