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Theorem eqvinc 2966
Description: A variable introduction law for class equality. (Contributed by NM, 14-Apr-1995.) (Proof shortened by Andrew Salmon, 8-Jun-2011.)
Hypothesis
Ref Expression
eqvinc.1
Assertion
Ref Expression
eqvinc
Distinct variable groups:   ,   ,

Proof of Theorem eqvinc
StepHypRef Expression
1 eqvinc.1 . . . . 5
21isseti 2865 . . . 4
3 ax-1 5 . . . . . 6
4 eqtr 2370 . . . . . . 7
54ex 423 . . . . . 6
63, 5jca 518 . . . . 5
76eximi 1576 . . . 4
8 pm3.43 832 . . . . 5
98eximi 1576 . . . 4
102, 7, 9mp2b 9 . . 3
111019.37aiv 1900 . 2
12 eqtr2 2371 . . 3
1312exlimiv 1634 . 2
1411, 13impbii 180 1
Colors of variables: wff setvar class
Syntax hints:   wi 4   wb 176   wa 358  wex 1541   wceq 1642   wcel 1710  cvv 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-11 1746  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-v 2861
This theorem is referenced by:  eqvincf  2967  preaddccan2lem1  4454  dff13  5471  nncdiv3lem1  6275
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