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Theorem equveli 2088
 Description: A variable elimination law for equality with no distinct variable requirements. (Compare equvini 2086.) (Contributed by NM, 1-Mar-2013.) (Proof shortened by Mario Carneiro, 17-Oct-2016.) (Proof shortened by Wolf Lammen, 15-Apr-2018.)
Assertion
Ref Expression
equveli

Proof of Theorem equveli
StepHypRef Expression
1 nfeqf 2012 . . . . 5
2 a9e 1955 . . . . . . 7
3 bi2 191 . . . . . . . . 9
4 ax-8 1689 . . . . . . . . 9
53, 4syl6com 34 . . . . . . . 8
65pm2.43a 48 . . . . . . 7
72, 6eximii 1588 . . . . . 6
8719.35i 1612 . . . . 5
9 nf2 1891 . . . . . 6
109biimpi 188 . . . . 5
111, 8, 10syl2im 37 . . . 4
1211ex 425 . . 3
13 bi1 180 . . . . . 6
144com12 30 . . . . . 6
1513, 14syl6com 34 . . . . 5
1615pm2.43a 48 . . . 4
1716al2imi 1571 . . 3
186al2imi 1571 . . 3
1912, 17, 18pm2.61ii 160 . 2
201919.21bi 1776 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 178   wa 360  wal 1550  wex 1551  wnf 1554 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953 This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552  df-nf 1555
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