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Mirrors > Home > ILE Home > Th. List > vtocl | GIF version |
Description: Implicit substitution of a class for a setvar variable. (Contributed by NM, 30-Aug-1993.) |
Ref | Expression |
---|---|
vtocl.1 | ⊢ 𝐴 ∈ V |
vtocl.2 | ⊢ (𝑥 = 𝐴 → (𝜑 ↔ 𝜓)) |
vtocl.3 | ⊢ 𝜑 |
Ref | Expression |
---|---|
vtocl | ⊢ 𝜓 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1467 | . 2 ⊢ Ⅎ𝑥𝜓 | |
2 | vtocl.1 | . 2 ⊢ 𝐴 ∈ V | |
3 | vtocl.2 | . 2 ⊢ (𝑥 = 𝐴 → (𝜑 ↔ 𝜓)) | |
4 | vtocl.3 | . 2 ⊢ 𝜑 | |
5 | 1, 2, 3, 4 | vtoclf 2673 | 1 ⊢ 𝜓 |
Colors of variables: wff set class |
Syntax hints: → wi 4 ↔ wb 104 = wceq 1290 ∈ wcel 1439 Vcvv 2620 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1382 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-4 1446 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-ext 2071 |
This theorem depends on definitions: df-bi 116 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-v 2622 |
This theorem is referenced by: vtoclb 2677 zfauscl 3965 bnd2 4014 uniex 4273 ordtriexmid 4351 onsucsssucexmid 4356 regexmid 4364 ordsoexmid 4391 onintexmid 4401 reg3exmid 4408 nnregexmid 4447 acexmidlemv 5664 caovcan 5823 findcard2 6659 findcard2s 6660 inffiexmid 6676 bj-uniex 12081 bj-omtrans 12124 |
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