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Theorem bj-drnf2v 36415
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.)
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 1917 1 (∀𝑥 𝑥 = 𝑦 → (Ⅎ𝑧𝜑 ↔ Ⅎ𝑧𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 205  wal 1531  wnf 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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