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Theorem equveli 2180
 Description: A variable elimination law for equality with no distinct variable requirements. Compare equvini 2179. (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 1690 . 2
2 ax6e 2094 . . . 4
3 biimpr 202 . . . . . 6
4 ax7 1860 . . . . . 6
53, 4syli 38 . . . . 5
65com12 32 . . . 4
72, 6eximii 1709 . . 3
8719.35i 1741 . 2
94spsd 1945 . . . . 5
109sps 1943 . . . 4
1110a1dd 47 . . 3
12 nfeqf 2139 . . . . 5
131219.9d 1968 . . . 4
1413ex 436 . . 3
1511, 14bija 357 . 2
161, 8, 15sylc 62 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 188   wa 371  wal 1442  wex 1663 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-10 1915  ax-12 1933  ax-13 2091 This theorem depends on definitions:  df-bi 189  df-an 373  df-ex 1664  df-nf 1668 This theorem is referenced by: (None)
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