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Theorem bj-drnf2v 34029
Description: Version of drnf2 2458 with a disjoint variable condition, which does not require ax-10 2136, ax-11 2151, ax-12 2167, ax-13 2381. Instance of nfbidv 1914. Note that the version of axc15 2435 with a disjoint variable condition is actually ax12v2 2169 (up to adding a superfluous antecedent). (Contributed by BJ, 17-Jun-2019.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
bj-drnf2v.1 (∀𝑥 𝑥 = 𝑦 → (𝜑𝜓))
Assertion
Ref Expression
bj-drnf2v (∀𝑥 𝑥 = 𝑦 → (Ⅎ𝑧𝜑 ↔ Ⅎ𝑧𝜓))
Distinct variable group:   𝑥,𝑦,𝑧
Allowed substitution hints:   𝜑(𝑥,𝑦,𝑧)   𝜓(𝑥,𝑦,𝑧)

Proof of Theorem bj-drnf2v
StepHypRef Expression
1 bj-drnf2v.1 . 2 (∀𝑥 𝑥 = 𝑦 → (𝜑𝜓))
21nfbidv 1914 1 (∀𝑥 𝑥 = 𝑦 → (Ⅎ𝑧𝜑 ↔ Ⅎ𝑧𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 207  wal 1526  wnf 1775
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902
This theorem depends on definitions:  df-bi 208  df-ex 1772  df-nf 1776
This theorem is referenced by: (None)
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