Theorem imass2d 46090

Description: Subset theorem for image. (Contributed by Glauco Siliprandi, 2-Jan-2022.)

Hypothesis

Ref	Expression
imass2d.1	⊢ (𝜑 → 𝐴 ⊆ 𝐵)

Assertion

Ref	Expression
imass2d	⊢ (𝜑 → (𝐶 “ 𝐴) ⊆ (𝐶 “ 𝐵))

Proof of Theorem imass2d

Step	Hyp	Ref	Expression
1		imass2d.1	. 2 ⊢ (𝜑 → 𝐴 ⊆ 𝐵)
2		imass2 6098	. 2 ⊢ (𝐴 ⊆ 𝐵 → (𝐶 “ 𝐴) ⊆ (𝐶 “ 𝐵))
3	1, 2	syl 18	1 ⊢ (𝜑 → (𝐶 “ 𝐴) ⊆ (𝐶 “ 𝐵))

This proof depends on syntax axioms:   → wi 4   ⊆ wss 3899   “ cima 5658

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2147  ax-9 2155  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-3an 1105  df-tru 1573  df-fal 1583  df-ex 1813  df-sb 2100  df-clab 2739  df-cleq 2752  df-clel 2835  df-rab 3413  df-v 3452  df-dif 3902  df-un 3904  df-in 3906  df-ss 3916  df-nul 4280  df-if 4483  df-sn 4585  df-pr 4587  df-op 4591  df-br 5104  df-opab 5168  df-xp 5661  df-cnv 5663  df-dm 5665  df-rn 5666  df-res 5667  df-ima 5668

This theorem is used by:  liminflelimsuplem  46603