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Theorem moeq 3012
 Description: There is at most one set equal to a class. (Contributed by NM, 8-Mar-1995.)
Assertion
Ref Expression
moeq ∃*x x = A
Distinct variable group:   x,A

Proof of Theorem moeq
StepHypRef Expression
1 isset 2863 . . . 4 (A V ↔ x x = A)
2 eueq 3008 . . . 4 (A V ↔ ∃!x x = A)
31, 2bitr3i 242 . . 3 (x x = A∃!x x = A)
43biimpi 186 . 2 (x x = A∃!x x = A)
5 df-mo 2209 . 2 (∃*x x = A ↔ (x x = A∃!x x = A))
64, 5mpbir 200 1 ∃*x x = A
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∃wex 1541   = wceq 1642   ∈ wcel 1710  ∃!weu 2204  ∃*wmo 2205  Vcvv 2859 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-mo 2209  df-clab 2340  df-cleq 2346  df-clel 2349  df-v 2861 This theorem is referenced by:  mosub  3014  euxfr2  3021  reueq  3033  funopabeq  5140  funsn  5147  fvopab4g  5388  ov2ag  5598  ov3  5599  ov6g  5600  ovmpt4g  5710  ovmpt2x  5712  fnce  6176
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