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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-drnf2v | Structured version Visualization version GIF version |
Description: Version of drnf2 2318 with a dv condition, which does not require ax-13 2234. Could be labeled "nfbidv". Note that the version of axc15 2291 with a dv condition is actually ax12v2 2036 (up to adding a superfluous antecedent). (Contributed by BJ, 17-Jun-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-drnf2v.1 | ⊢ (∀𝑥 𝑥 = 𝑦 → (𝜑 ↔ 𝜓)) |
Ref | Expression |
---|---|
bj-drnf2v | ⊢ (∀𝑥 𝑥 = 𝑦 → (Ⅎ𝑧𝜑 ↔ Ⅎ𝑧𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1830 | . 2 ⊢ Ⅎ𝑧∀𝑥 𝑥 = 𝑦 | |
2 | bj-drnf2v.1 | . 2 ⊢ (∀𝑥 𝑥 = 𝑦 → (𝜑 ↔ 𝜓)) | |
3 | 1, 2 | nfbidf 2079 | 1 ⊢ (∀𝑥 𝑥 = 𝑦 → (Ⅎ𝑧𝜑 ↔ Ⅎ𝑧𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 195 ∀wal 1473 Ⅎwnf 1699 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-12 2034 |
This theorem depends on definitions: df-bi 196 df-ex 1696 df-nf 1701 |
This theorem is referenced by: (None) |
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