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Theorem equveli 2088
Description: A variable elimination law for equality with no distinct variable requirements. (Compare equvini 2087.) (Contributed by NM, 1-Mar-2013.) (Proof shortened by Mario Carneiro, 17-Oct-2016.) (Proof shortened by Wolf Lammen, 15-Jun-2019.)
Assertion
Ref Expression
equveli

Proof of Theorem equveli
StepHypRef Expression
1 albi 1639 . 2
2 ax6e 2002 . . . 4
3 bi2 198 . . . . . 6
4 ax-7 1790 . . . . . 6
53, 4syli 37 . . . . 5
65com12 31 . . . 4
72, 6eximii 1658 . . 3
8719.35i 1689 . 2
94spsd 1867 . . . . 5
109sps 1865 . . . 4
1110a1dd 46 . . 3
12 nfeqf 2045 . . . . 5
131219.9d 1892 . . . 4
1413ex 434 . . 3
1511, 14bija 355 . 2
161, 8, 15sylc 60 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  E.wex 1612
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-12 1854  ax-13 1999
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617
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