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Theorem sbbi 2142
Description: Equivalence inside and outside of a substitution are equivalent. (Contributed by NM, 14-May-1993.)
Assertion
Ref Expression
sbbi

Proof of Theorem sbbi
StepHypRef Expression
1 dfbi2 628 . . 3
21sbbii 1746 . 2
3 sbim 2136 . . . 4
4 sbim 2136 . . . 4
53, 4anbi12i 697 . . 3
6 sban 2140 . . 3
7 dfbi2 628 . . 3
85, 6, 73bitr4i 277 . 2
92, 8bitri 249 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  [wsb 1739
This theorem is referenced by:  spsbbi  2143  sblbis  2145  sbrbis  2146  sbieOLD  2150  sbidmOLD  2157  pm13.183  3240  sbcbig  3374  sb8iota  5563
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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