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Theorem bj-cbv3hv2 31915
 Description: Version of cbv3h 2254 with two dv conditions, which does not require ax-11 2021 nor ax-13 2234. (Contributed by BJ, 24-Jun-2019.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
bj-cbv3hv2.nf (𝜓 → ∀𝑥𝜓)
bj-cbv3hv2.1 (𝑥 = 𝑦 → (𝜑𝜓))
Assertion
Ref Expression
bj-cbv3hv2 (∀𝑥𝜑 → ∀𝑦𝜓)
Distinct variable groups:   𝑥,𝑦   𝜑,𝑦
Allowed substitution hints:   𝜑(𝑥)   𝜓(𝑥,𝑦)

Proof of Theorem bj-cbv3hv2
StepHypRef Expression
1 bj-cbv3hv2.nf . . 3 (𝜓 → ∀𝑥𝜓)
21nf5i 2011 . 2 𝑥𝜓
3 bj-cbv3hv2.1 . 2 (𝑥 = 𝑦 → (𝜑𝜓))
42, 3bj-cbv3v2 31914 1 (∀𝑥𝜑 → ∀𝑦𝜓)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1473 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-10 2006  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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