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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 2121 . . 3
43imbi2i 312 . 2
51, 4bitri 249 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  F/wnf 1616  [wsb 1739
This theorem is referenced by:  sbmo  2335
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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