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Theorem fvilbd 38500
 Description: A set is a subset of its image under the identity relation. (Contributed by RP, 22-Jul-2020.)
Hypothesis
Ref Expression
fvilbd.r (𝜑𝑅 ∈ V)
Assertion
Ref Expression
fvilbd (𝜑𝑅 ⊆ ( I ‘𝑅))

Proof of Theorem fvilbd
StepHypRef Expression
1 ssid 3771 . 2 𝑅𝑅
2 fvilbd.r . . 3 (𝜑𝑅 ∈ V)
3 fvi 6397 . . 3 (𝑅 ∈ V → ( I ‘𝑅) = 𝑅)
42, 3syl 17 . 2 (𝜑 → ( I ‘𝑅) = 𝑅)
51, 4syl5sseqr 3801 1 (𝜑𝑅 ⊆ ( I ‘𝑅))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1630   ∈ wcel 2144  Vcvv 3349   ⊆ wss 3721   I cid 5156  ‘cfv 6031 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1869  ax-4 1884  ax-5 1990  ax-6 2056  ax-7 2092  ax-9 2153  ax-10 2173  ax-11 2189  ax-12 2202  ax-13 2407  ax-ext 2750  ax-sep 4912  ax-nul 4920  ax-pr 5034 This theorem depends on definitions:  df-bi 197  df-an 383  df-or 827  df-3an 1072  df-tru 1633  df-ex 1852  df-nf 1857  df-sb 2049  df-eu 2621  df-mo 2622  df-clab 2757  df-cleq 2763  df-clel 2766  df-nfc 2901  df-ral 3065  df-rex 3066  df-rab 3069  df-v 3351  df-sbc 3586  df-dif 3724  df-un 3726  df-in 3728  df-ss 3735  df-nul 4062  df-if 4224  df-sn 4315  df-pr 4317  df-op 4321  df-uni 4573  df-br 4785  df-opab 4845  df-id 5157  df-xp 5255  df-rel 5256  df-cnv 5257  df-co 5258  df-dm 5259  df-iota 5994  df-fun 6033  df-fv 6039 This theorem is referenced by: (None)
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