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Theorem sbor 2066
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 2065 . . 3
2 sbn 2062 . . . 4
32imbi1i 315 . . 3
41, 3bitri 240 . 2
5 df-or 359 . . 3
65sbbii 1653 . 2
7 df-or 359 . 2
84, 6, 73bitr4i 268 1
Colors of variables: wff setvar class
Syntax hints:   wn 3   wi 4   wb 176   wo 357  wsb 1648
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649
This theorem is referenced by:  sbcor  3090  sbcorg  3091  unab  3521
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