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Mirrors > Home > ILE Home > Th. List > sbequ6 | GIF version |
Description: Substitution does not change a distinctor. (Contributed by NM, 5-Aug-1993.) (Revised by NM, 14-May-2005.) |
Ref | Expression |
---|---|
sbequ6 | ⊢ ([𝑤 / 𝑧] ¬ ∀𝑥 𝑥 = 𝑦 ↔ ¬ ∀𝑥 𝑥 = 𝑦) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfnae 1702 | . 2 ⊢ Ⅎ𝑧 ¬ ∀𝑥 𝑥 = 𝑦 | |
2 | 1 | sbf 1757 | 1 ⊢ ([𝑤 / 𝑧] ¬ ∀𝑥 𝑥 = 𝑦 ↔ ¬ ∀𝑥 𝑥 = 𝑦) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 ↔ wb 104 ∀wal 1333 [wsb 1742 |
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-in1 604 ax-in2 605 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-fal 1341 df-nf 1441 df-sb 1743 |
This theorem is referenced by: (None) |
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