Theorem rnexd 7955

Description: The range of a set is a set. Deduction version of rnexd 7955. (Contributed by Thierry Arnoux, 14-Feb-2025.)

Hypothesis

Ref	Expression
rnexd.1	⊢ (𝜑 → 𝐴 ∈ 𝑉)

Assertion

Ref	Expression
rnexd	⊢ (𝜑 → ran 𝐴 ∈ V)

Proof of Theorem rnexd

Step	Hyp	Ref	Expression
1		rnexd.1	. 2 ⊢ (𝜑 → 𝐴 ∈ 𝑉)
2		rnexg 7942	. 2 ⊢ (𝐴 ∈ 𝑉 → ran 𝐴 ∈ V)
3	1, 2	syl 17	1 ⊢ (𝜑 → ran 𝐴 ∈ V)

Syntax hints:   → wi 4   ∈ wcel 2108  Vcvv 3488  ran crn 5701

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2711  ax-sep 5317  ax-nul 5324  ax-pr 5447  ax-un 7770

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 847  df-3an 1089  df-tru 1540  df-fal 1550  df-ex 1778  df-sb 2065  df-clab 2718  df-cleq 2732  df-clel 2819  df-rab 3444  df-v 3490  df-dif 3979  df-un 3981  df-in 3983  df-ss 3993  df-nul 4353  df-if 4549  df-sn 4649  df-pr 4651  df-op 4655  df-uni 4932  df-br 5167  df-opab 5229  df-cnv 5708  df-dm 5710  df-rn 5711

This theorem is referenced by:  qusrn  33402