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Theorem bj-cbv3hv2 33047
Description: Version of cbv3h 2441 with two dv conditions, which does not require ax-11 2202 nor ax-13 2422. (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 2191 . 2 𝑥𝜓
3 bj-cbv3hv2.1 . 2 (𝑥 = 𝑦 → (𝜑𝜓))
42, 3cbv3v2 2348 1 (∀𝑥𝜑 → ∀𝑦𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1635
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1877  ax-4 1894  ax-5 2001  ax-6 2069  ax-7 2105  ax-10 2186  ax-12 2215
This theorem depends on definitions:  df-bi 198  df-ex 1860  df-nf 1864
This theorem is referenced by: (None)
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