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Theorem dfsb2 2108
 Description: An alternate definition of proper substitution that, like df-sb 1659, mixes free and bound variables to avoid distinct variable requirements. (Contributed by NM, 17-Feb-2005.)
Assertion
Ref Expression
dfsb2

Proof of Theorem dfsb2
StepHypRef Expression
1 sp 1763 . . . 4
2 sbequ2 1660 . . . . 5
32sps 1770 . . . 4
4 orc 375 . . . 4
51, 3, 4ee12an 1372 . . 3
6 sb4 2093 . . . 4
7 olc 374 . . . 4
86, 7syl6 31 . . 3
95, 8pm2.61i 158 . 2
10 sbequ1 1943 . . . 4
1110imp 419 . . 3
12 sb2 2090 . . 3
1311, 12jaoi 369 . 2
149, 13impbii 181 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177   wo 358   wa 359  wal 1549  wsb 1658 This theorem is referenced by:  dfsb3  2109 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659
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