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Theorem sbbi 1833
 Description: Equivalence inside and outside of a substitution are equivalent. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
sbbi

Proof of Theorem sbbi
StepHypRef Expression
1 dfbi2 368 . . 3
21sbbii 1648 . 2
3 sbim 1827 . . . 4
4 sbim 1827 . . . 4
53, 4anbi12i 433 . . 3
6 sban 1829 . . 3
7 dfbi2 368 . . 3
85, 6, 73bitr4i 201 . 2
92, 8bitri 173 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98  wsb 1645 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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646 This theorem is referenced by:  sblbis  1834  sbrbis  1835  sbco  1842  sbcocom  1844  elsb3  1852  elsb4  1853  sb8eu  1913  sb8euh  1923  pm13.183  2681  sbcbig  2809  sb8iota  4874
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