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Theorem zfpair2 3973
 Description: Derive the abbreviated version of the Axiom of Pairing from ax-pr 3972. (Contributed by NM, 14-Nov-2006.)
Assertion
Ref Expression
zfpair2

Proof of Theorem zfpair2
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 ax-pr 3972 . . . 4
21bm1.3ii 3906 . . 3
3 dfcleq 2050 . . . . 5
4 vex 2577 . . . . . . . 8
54elpr 3424 . . . . . . 7
65bibi2i 220 . . . . . 6
76albii 1375 . . . . 5
83, 7bitri 177 . . . 4
98exbii 1512 . . 3
102, 9mpbir 138 . 2
1110issetri 2581 1
 Colors of variables: wff set class Syntax hints:   wb 102   wo 639  wal 1257   wceq 1259  wex 1397   wcel 1409  cvv 2574  cpr 3404 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-14 1421  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038  ax-sep 3903  ax-pr 3972 This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-v 2576  df-un 2950  df-sn 3409  df-pr 3410 This theorem is referenced by:  prexgOLD  3974  prexg  3975  onintexmid  4325  funopg  4962
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