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Theorem sblim 2246
 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 2244 . 2
2 sblim.1 . . . 4
32sbf 2229 . . 3
43imbi2i 319 . 2
51, 4bitri 257 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 189  wnf 1675  wsb 1805 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-12 1950  ax-13 2104 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-ex 1672  df-nf 1676  df-sb 1806 This theorem is referenced by:  sbmo  2364
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