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Theorem sbbi 1963
 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 612 . . 3
21sbbii 1885 . 2
3 sbim 1957 . . . 4
4 sbim 1957 . . . 4
53, 4anbi12i 681 . . 3
6 sban 1961 . . 3
7 dfbi2 612 . . 3
85, 6, 73bitr4i 270 . 2
92, 8bitri 242 1
 Colors of variables: wff set class Syntax hints:   wi 6   wb 178   wa 360  wsb 1882 This theorem is referenced by:  sblbis  1964  sbrbis  1965  a4sbbi  1969  sbco  1977  sbidm  1979  sbal  2087  sb8eu  2132  pm13.183  2845  sbcbig  2967  sb8iota  6150 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692 This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883
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