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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-drnf2v | Structured version Visualization version GIF version |
Description: Version of drnf2 2437 with a disjoint variable condition, which does not require ax-10 2129, ax-11 2146, ax-12 2166, ax-13 2365. Instance of nfbidv 1917. Note that the version of axc15 2415 with a disjoint variable condition is actually ax12v2 2168 (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 | bj-drnf2v.1 | . 2 ⊢ (∀𝑥 𝑥 = 𝑦 → (𝜑 ↔ 𝜓)) | |
2 | 1 | nfbidv 1917 | 1 ⊢ (∀𝑥 𝑥 = 𝑦 → (Ⅎ𝑧𝜑 ↔ Ⅎ𝑧𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 205 ∀wal 1531 Ⅎwnf 1777 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 |
This theorem depends on definitions: df-bi 206 df-ex 1774 df-nf 1778 |
This theorem is referenced by: (None) |
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