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Theorem bj-cbvalvv 31920
Description: Version of cbvalv 2261 with a dv condition, which does not require ax-13 2234. UPDATE: this is cbvalvw 1956 (which is proved with fewer axioms). (Contributed by BJ, 31-May-2019.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
bj-cbvalvv.1 (𝑥 = 𝑦 → (𝜑𝜓))
Assertion
Ref Expression
bj-cbvalvv (∀𝑥𝜑 ↔ ∀𝑦𝜓)
Distinct variable groups:   𝑥,𝑦   𝜑,𝑦   𝜓,𝑥
Allowed substitution hints:   𝜑(𝑥)   𝜓(𝑦)

Proof of Theorem bj-cbvalvv
StepHypRef Expression
1 nfv 1830 . 2 𝑦𝜑
2 nfv 1830 . 2 𝑥𝜓
3 bj-cbvalvv.1 . 2 (𝑥 = 𝑦 → (𝜑𝜓))
41, 2, 3cbvalv1 2163 1 (∀𝑥𝜑 ↔ ∀𝑦𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 195  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-11 2021  ax-12 2034
This theorem depends on definitions:  df-bi 196  df-an 385  df-ex 1696  df-nf 1701
This theorem is referenced by:  bj-zfpow  31983  bj-nfcjust  32044
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