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Theorem sbbi 2146
 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 611 . . 3
21sbbii 1667 . 2
3 sbim 2139 . . . 4
4 sbim 2139 . . . 4
53, 4anbi12i 680 . . 3
6 sban 2144 . . 3
7 dfbi2 611 . . 3
85, 6, 73bitr4i 270 . 2
92, 8bitri 242 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360  wsb 1659 This theorem is referenced by:  spsbbi  2147  sblbis  2149  sbrbis  2150  sbieALT  2155  sbco  2164  sbidm  2166  sbal  2210  sb8eu  2305  pm13.183  3082  sbcbig  3213  sb8iota  5454 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660
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