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Theorem sbor 1825
Description: Logical OR inside and outside of substitution are equivalent. (Contributed by NM, 29-Sep-2002.) (Proof rewritten by Jim Kingdon, 3-Feb-2018.)
Assertion
Ref Expression
sbor

Proof of Theorem sbor
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sborv 1767 . . . 4
21sbbii 1645 . . 3
3 sborv 1767 . . 3
42, 3bitri 173 . 2
5 ax-17 1416 . . 3
65sbco2v 1818 . 2
7 ax-17 1416 . . . 4
87sbco2v 1818 . . 3
9 ax-17 1416 . . . 4
109sbco2v 1818 . . 3
118, 10orbi12i 680 . 2
124, 6, 113bitr3i 199 1
Colors of variables: wff set class
Syntax hints:   wb 98   wo 628  wsb 1642
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643
This theorem is referenced by:  sbcor  2801  sbcorg  2802  unab  3198
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