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Theorem dveeq2or 1697
 Description: Quantifier introduction when one pair of variables is distinct. Like dveeq2 1696 but connecting by a disjunction rather than negation and implication makes the theorem stronger in intuitionistic logic. (Contributed by Jim Kingdon, 1-Feb-2018.)
Assertion
Ref Expression
dveeq2or
Distinct variable group:   ,

Proof of Theorem dveeq2or
StepHypRef Expression
1 ax-i12 1398 . . . . . 6
2 orass 684 . . . . . 6
31, 2mpbir 134 . . . . 5
4 pm1.4 646 . . . . . 6
54orim1i 677 . . . . 5
63, 5ax-mp 7 . . . 4
7 orass 684 . . . 4
86, 7mpbi 133 . . 3
9 ax16 1694 . . . . . 6
109a5i 1435 . . . . 5
11 id 19 . . . . 5
1210, 11jaoi 636 . . . 4
1312orim2i 678 . . 3
148, 13ax-mp 7 . 2
15 df-nf 1350 . . . 4
1615biimpri 124 . . 3
1716orim2i 678 . 2
1814, 17ax-mp 7 1
 Colors of variables: wff set class Syntax hints:   wi 4   wo 629  wal 1241  wnf 1349 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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646 This theorem is referenced by:  equs5or  1711  sbal1yz  1877  copsexg  3981
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