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Theorem bj-chvarv 33260
 Description: Version of chvar 2417 with a disjoint variable condition, which does not require ax-13 2391. (Contributed by BJ, 31-May-2019.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
bj-chvarv.nf 𝑥𝜓
bj-chvarv.1 (𝑥 = 𝑦 → (𝜑𝜓))
bj-chvarv.2 𝜑
Assertion
Ref Expression
bj-chvarv 𝜓
Distinct variable group:   𝑥,𝑦
Allowed substitution hints:   𝜑(𝑥,𝑦)   𝜓(𝑥,𝑦)

Proof of Theorem bj-chvarv
StepHypRef Expression
1 bj-chvarv.nf . . 3 𝑥𝜓
2 bj-chvarv.1 . . . 4 (𝑥 = 𝑦 → (𝜑𝜓))
32biimpd 221 . . 3 (𝑥 = 𝑦 → (𝜑𝜓))
41, 3spimv1 2298 . 2 (∀𝑥𝜑𝜓)
5 bj-chvarv.2 . 2 𝜑
64, 5mpg 1898 1 𝜓
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 198  Ⅎwnf 1884 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1896  ax-4 1910  ax-5 2011  ax-6 2077  ax-7 2114  ax-12 2222 This theorem depends on definitions:  df-bi 199  df-ex 1881  df-nf 1885 This theorem is referenced by:  bj-axrep2  33315  bj-axrep3  33316
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