Mathbox for Norm Megill < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  equviniNEW7 Structured version   Unicode version

Theorem equviniNEW7 29625
 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
equviniNEW7

Proof of Theorem equviniNEW7
StepHypRef Expression
1 equcomi 1693 . . . . . 6
21alimi 1569 . . . . 5
3 a9eNEW7 29568 . . . . 5
42, 3jctir 526 . . . 4
54a1d 24 . . 3
6 19.29 1607 . . 3
75, 6syl6 32 . 2
8 a9eNEW7 29568 . . . . . 6
98, 1eximii 1588 . . . . 5
109a1ii 26 . . . 4
1110anc2ri 543 . . 3
12 19.29r 1608 . . 3
1311, 12syl6 32 . 2
14 ioran 478 . . 3
15 nfeqfNEW7 29584 . . . 4
16 ax-8 1689 . . . . . 6
1716anc2li 542 . . . . 5
1817equcoms 1695 . . . 4
1915, 18spimedNEW7 29608 . . 3
2014, 19sylbi 189 . 2
217, 13, 20ecase3 909 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wo 359   wa 360  wal 1550  wex 1551 This theorem is referenced by:  equvinNEW7  29627  sbequiNEW7  29677 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-11 1763  ax-12 1953  ax-7v 29540 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555
 Copyright terms: Public domain W3C validator