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Theorem equvini 2087
 Description: A variable introduction law for equality. Lemma 15 of [Monk2] p. 109, however we do not require to be distinct from and . See equvin 1804 for a shorter proof requiring fewer axioms when is required to be distinct from and . (Contributed by NM, 10-Jan-1993.) (Proof shortened by Andrew Salmon, 25-May-2011.) (Proof shortened by Wolf Lammen, 15-Sep-2018.)
Assertion
Ref Expression
equvini

Proof of Theorem equvini
StepHypRef Expression
1 equtr 1796 . . . 4
2 equequ2 1799 . . . . . 6
32biimprd 223 . . . . 5
43anc2ri 558 . . . 4
51, 4syli 37 . . 3
6 19.8a 1857 . . 3
75, 6syl6 33 . 2
8 ax13 2047 . . 3
9 ax6e 2002 . . . . 5
109, 4eximii 1658 . . . 4
111019.35i 1689 . . 3
128, 11syl6 33 . 2
137, 12pm2.61i 164 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  ->wi 4  /\wa 369  A.wal 1393  E.wex 1612 This theorem is referenced by:  equvinOLD  2090  2ax6elem  2193 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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