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Theorem bj-cbv3hv2 32423
Description: Version of cbv3h 2265 with two dv conditions, which does not require ax-11 2031 nor ax-13 2245. (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 2021 . 2 𝑥𝜓
3 bj-cbv3hv2.1 . 2 (𝑥 = 𝑦 → (𝜑𝜓))
42, 3bj-cbv3v2 32422 1 (∀𝑥𝜑 → ∀𝑦𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1478
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-10 2016  ax-12 2044
This theorem depends on definitions:  df-bi 197  df-ex 1702  df-nf 1707
This theorem is referenced by: (None)
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