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Mirrors > Home > MPE Home > Th. List > vtoclALT | Structured version Visualization version GIF version |
Description: Alternate proof of vtocl 3259. Shorter but requires more axioms. (Contributed by NM, 30-Aug-1993.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
vtocl.1 | ⊢ 𝐴 ∈ V |
vtocl.2 | ⊢ (𝑥 = 𝐴 → (𝜑 ↔ 𝜓)) |
vtocl.3 | ⊢ 𝜑 |
Ref | Expression |
---|---|
vtoclALT | ⊢ 𝜓 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1843 | . 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 3258 | 1 ⊢ 𝜓 |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 196 = wceq 1483 ∈ wcel 1990 Vcvv 3200 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-12 2047 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-v 3202 |
This theorem is referenced by: (None) |
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