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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 1715 | . 2 ⊢ Ⅎ𝑧 ¬ ∀𝑥 𝑥 = 𝑦 | |
2 | 1 | sbf 1770 | 1 ⊢ ([𝑤 / 𝑧] ¬ ∀𝑥 𝑥 = 𝑦 ↔ ¬ ∀𝑥 𝑥 = 𝑦) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 ↔ wb 104 ∀wal 1346 [wsb 1755 |
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 609 ax-in2 610 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-fal 1354 df-nf 1454 df-sb 1756 |
This theorem is referenced by: (None) |
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