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Mirrors > Home > ILE Home > Th. List > dveeq1 | Unicode version |
Description: Quantifier introduction when one pair of variables is distinct. (Contributed by NM, 2-Jan-2002.) (Proof rewritten by Jim Kingdon, 19-Feb-2018.) |
Ref | Expression |
---|---|
dveeq1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dveeq2 1787 | . 2 | |
2 | equcom 1682 | . 2 | |
3 | 2 | albii 1446 | . 2 |
4 | 1, 2, 3 | 3imtr3g 203 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wal 1329 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 |
This theorem is referenced by: sbal2 1995 |
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