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Theorem equvini 1638
Description: A variable introduction law for equality. Lemma 15 of [Monk2] p. 109, however we do not require to be distinct from and (making the proof longer). (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 25-May-2011.)
Assertion
Ref Expression
equvini

Proof of Theorem equvini
StepHypRef Expression
1 ax12or 1400 . 2
2 equcomi 1589 . . . . . . 7
32alimi 1341 . . . . . 6
4 a9e 1583 . . . . . 6
53, 4jctir 296 . . . . 5
65a1d 22 . . . 4
7 19.29 1508 . . . 4
86, 7syl6 29 . . 3
9 a9e 1583 . . . . . . . 8
102eximi 1488 . . . . . . . 8
119, 10ax-mp 7 . . . . . . 7
1211a1ii 24 . . . . . 6
1312anc2ri 313 . . . . 5
14 19.29r 1509 . . . . 5
1513, 14syl6 29 . . . 4
16 ax-8 1392 . . . . . . . . . . . 12
1716anc2li 312 . . . . . . . . . . 11
1817equcoms 1591 . . . . . . . . . 10
1918com12 27 . . . . . . . . 9
2019alimi 1341 . . . . . . . 8
21 exim 1487 . . . . . . . 8
2220, 21syl 14 . . . . . . 7
239, 22mpi 15 . . . . . 6
2423imim2i 12 . . . . 5
2524sps 1427 . . . 4
2615, 25jaoi 635 . . 3
278, 26jaoi 635 . 2
281, 27ax-mp 7 1
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wo 628  wal 1240   wceq 1242  wex 1378
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-i12 1395  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  sbequi  1717  equvin  1740
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