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Theorem fvilbd 41279
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 3948 . 2 𝑅𝑅
2 fvilbd.r . . 3 (𝜑𝑅 ∈ V)
3 fvi 6841 . . 3 (𝑅 ∈ V → ( I ‘𝑅) = 𝑅)
42, 3syl 17 . 2 (𝜑 → ( I ‘𝑅) = 𝑅)
51, 4sseqtrrid 3979 1 (𝜑𝑅 ⊆ ( I ‘𝑅))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1542  wcel 2110  Vcvv 3431  wss 3892   I cid 5489  cfv 6432
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 1975  ax-7 2015  ax-8 2112  ax-9 2120  ax-10 2141  ax-11 2158  ax-12 2175  ax-ext 2711  ax-sep 5227  ax-nul 5234  ax-pr 5356
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-3an 1088  df-tru 1545  df-fal 1555  df-ex 1787  df-nf 1791  df-sb 2072  df-mo 2542  df-eu 2571  df-clab 2718  df-cleq 2732  df-clel 2818  df-nfc 2891  df-ral 3071  df-rex 3072  df-rab 3075  df-v 3433  df-dif 3895  df-un 3897  df-in 3899  df-ss 3909  df-nul 4263  df-if 4466  df-sn 4568  df-pr 4570  df-op 4574  df-uni 4846  df-br 5080  df-opab 5142  df-id 5490  df-xp 5596  df-rel 5597  df-cnv 5598  df-co 5599  df-dm 5600  df-iota 6390  df-fun 6434  df-fv 6440
This theorem is referenced by: (None)
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