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Theorem dfsb2 2114
Description: An alternate definition of proper substitution that, like df-sb 1740, 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 1859 . . . 4
2 sbequ2 1741 . . . . 5
32sps 1865 . . . 4
4 orc 385 . . . 4
51, 3, 4syl6an 545 . . 3
6 sb4 2097 . . . 4
7 olc 384 . . . 4
86, 7syl6 33 . . 3
95, 8pm2.61i 164 . 2
10 sbequ1 1991 . . . 4
1110imp 429 . . 3
12 sb2 2093 . . 3
1311, 12jaoi 379 . 2
149, 13impbii 188 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  <->wb 184  \/wo 368  /\wa 369  A.wal 1393  [wsb 1739
This theorem is referenced by:  dfsb3  2115
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-or 370  df-an 371  df-ex 1613  df-nf 1617  df-sb 1740
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