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Theorem sbor 2139
Description: Logical OR inside and outside of substitution are equivalent. (Contributed by NM, 29-Sep-2002.)
Assertion
Ref Expression
sbor

Proof of Theorem sbor
StepHypRef Expression
1 sbim 2136 . . 3
2 sbn 2132 . . . 4
32imbi1i 325 . . 3
41, 3bitri 249 . 2
5 df-or 370 . . 3
65sbbii 1746 . 2
7 df-or 370 . 2
84, 6, 73bitr4i 277 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  <->wb 184  \/wo 368  [wsb 1739
This theorem is referenced by:  sbcor  3372  sbcorgOLD  3373  unab  3764
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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