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Theorem equveli 2061
 Description: A variable elimination law for equality with no distinct variable requirements. (Compare equvini 2060.) (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 ax6e 1971 . . . 4
2 bi2 198 . . . . . 6
3 ax-7 1739 . . . . . 6
42, 3syli 37 . . . . 5
54com12 31 . . . 4
61, 5eximii 1637 . . 3
7619.35i 1666 . 2
8 albi 1619 . . 3
93spsd 1816 . . . . . 6
109sps 1814 . . . . 5
1110a1dd 46 . . . 4
12 nfeqf 2018 . . . . . 6
131219.9d 1840 . . . . 5
1413ex 434 . . . 4
1511, 14bija 355 . . 3
168, 15syl 16 . 2
177, 16mpd 15 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 184   wa 369  wal 1377  wex 1596 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-12 1803  ax-13 1968 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1597  df-nf 1600 This theorem is referenced by: (None)
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