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Theorem dveeq2or 1679
 Description: Quantifier introduction when one pair of variables is distinct. Like dveeq2 1678 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 1379 . . . . . 6
2 orass 671 . . . . . 6
31, 2mpbir 134 . . . . 5
4 pm1.4 633 . . . . . 6
54orim1i 664 . . . . 5
63, 5ax-mp 7 . . . 4
7 orass 671 . . . 4
86, 7mpbi 133 . . 3
9 ax16 1676 . . . . . 6
109a5i 1417 . . . . 5
11 id 19 . . . . 5
1210, 11jaoi 623 . . . 4
1312orim2i 665 . . 3
148, 13ax-mp 7 . 2
15 df-nf 1330 . . . 4
1615biimpri 124 . . 3
1716orim2i 665 . 2
1814, 17ax-mp 7 1
 Colors of variables: wff set class Syntax hints:   wi 4   wo 616  wal 1226  wnf 1329 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 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409 This theorem depends on definitions:  df-bi 110  df-nf 1330  df-sb 1628 This theorem is referenced by:  equs5or  1693  sbal1yz  1859  copsexg  3955
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