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Theorem sblim 2138
 Description: Substitution with a variable not free in consequent affects only the antecedent. (Contributed by NM, 14-Nov-2013.) (Revised by Mario Carneiro, 4-Oct-2016.)
Hypothesis
Ref Expression
sblim.1
Assertion
Ref Expression
sblim

Proof of Theorem sblim
StepHypRef Expression
1 sbim 2136 . 2
2 sblim.1 . . . 4
32sbf 2118 . . 3
43imbi2i 305 . 2
51, 4bitri 242 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178  wnf 1554  wsb 1659 This theorem is referenced by:  sbnf2  2185  sbmo  2312 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951 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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