Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  sbrim Structured version   Unicode version

Theorem sbrim 2138
 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 2137 . 2
2 sbrim.1 . . . 4
32sbf 2119 . . 3
43imbi1i 317 . 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:  sbiedALT  2154  sbco2d  2164 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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
 Copyright terms: Public domain W3C validator