Theorem rele 4796

Description: The membership relation is a relation. (Contributed by NM, 26-Apr-1998.) (Revised by Mario Carneiro, 21-Dec-2013.)

Assertion

Ref	Expression
rele	⊢ Rel E

Proof of Theorem rele

Dummy variables 𝑥 𝑦 are mutually distinct and distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-eprel 4324	. 2 ⊢ E = {⟨𝑥, 𝑦⟩ ∣ 𝑥 ∈ 𝑦}
2	1	relopabi 4791	1 ⊢ Rel E

Syntax hints:   E cep 4322  Rel wrel 4668

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-10 1519  ax-11 1520  ax-i12 1521  ax-bndl 1523  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549  ax-14 2170  ax-ext 2178  ax-sep 4151  ax-pow 4207  ax-pr 4242

This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1475  df-sb 1777  df-clab 2183  df-cleq 2189  df-clel 2192  df-nfc 2328  df-ral 2480  df-rex 2481  df-v 2765  df-un 3161  df-in 3163  df-ss 3170  df-pw 3607  df-sn 3628  df-pr 3629  df-op 3631  df-opab 4095  df-eprel 4324  df-xp 4669  df-rel 4670

This theorem is referenced by: (None)