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Theorem fvilbd 39899
 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 3993 . 2 𝑅𝑅
2 fvilbd.r . . 3 (𝜑𝑅 ∈ V)
3 fvi 6737 . . 3 (𝑅 ∈ V → ( I ‘𝑅) = 𝑅)
42, 3syl 17 . 2 (𝜑 → ( I ‘𝑅) = 𝑅)
51, 4sseqtrrid 4024 1 (𝜑𝑅 ⊆ ( I ‘𝑅))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1530   ∈ wcel 2107  Vcvv 3500   ⊆ wss 3940   I cid 5458  ‘cfv 6352 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1904  ax-6 1963  ax-7 2008  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2153  ax-12 2169  ax-ext 2798  ax-sep 5200  ax-nul 5207  ax-pr 5326 This theorem depends on definitions:  df-bi 208  df-an 397  df-or 844  df-3an 1083  df-tru 1533  df-ex 1774  df-nf 1778  df-sb 2063  df-mo 2620  df-eu 2652  df-clab 2805  df-cleq 2819  df-clel 2898  df-nfc 2968  df-ral 3148  df-rex 3149  df-rab 3152  df-v 3502  df-sbc 3777  df-dif 3943  df-un 3945  df-in 3947  df-ss 3956  df-nul 4296  df-if 4471  df-sn 4565  df-pr 4567  df-op 4571  df-uni 4838  df-br 5064  df-opab 5126  df-id 5459  df-xp 5560  df-rel 5561  df-cnv 5562  df-co 5563  df-dm 5564  df-iota 6312  df-fun 6354  df-fv 6360 This theorem is referenced by: (None)
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