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Theorem sbbi 2120
 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 610 . . 3
21sbbii 1661 . 2
3 sbim 2114 . . . 4
4 sbim 2114 . . . 4
53, 4anbi12i 679 . . 3
6 sban 2118 . . 3
7 dfbi2 610 . . 3
85, 6, 73bitr4i 269 . 2
92, 8bitri 241 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wsb 1655 This theorem is referenced by:  sblbis  2121  sbrbis  2122  spsbbi  2126  sbco  2132  sbidm  2134  sbal  2177  sb8eu  2272  pm13.183  3036  sbcbig  3167  sb8iota  5384 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656
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