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Theorem sbrim 2136
 Description: Substitution with a variable not free in antecedent affects only the consequent. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 4-Oct-2016.)
Hypothesis
Ref Expression
sbrim.1
Assertion
Ref Expression
sbrim

Proof of Theorem sbrim
StepHypRef Expression
1 sbim 2135 . 2
2 sbrim.1 . . . 4
32sbf 2117 . . 3
43imbi1i 316 . 2
51, 4bitri 241 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177  wnf 1553  wsb 1658 This theorem is referenced by:  sbied  2150  sbco2d  2162 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659
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