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Theorem hbaevg 1971
Description: Generalization of hbaev 1972, proved at no extra cost. Instance of aev2 1973. (Contributed by Wolf Lammen, 22-Mar-2021.) (Revised by BJ, 29-Mar-2021.)
Assertion
Ref Expression
hbaevg (∀𝑥 𝑥 = 𝑦 → ∀𝑧𝑡 𝑡 = 𝑢)
Distinct variable groups:   𝑥,𝑦   𝑢,𝑡

Proof of Theorem hbaevg
Dummy variables 𝑣 𝑤 are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 aevlem 1968 . 2 (∀𝑥 𝑥 = 𝑦 → ∀𝑣 𝑣 = 𝑤)
2 aevlem 1968 . . 3 (∀𝑣 𝑣 = 𝑤 → ∀𝑡 𝑡 = 𝑢)
32alrimiv 1842 . 2 (∀𝑣 𝑣 = 𝑤 → ∀𝑧𝑡 𝑡 = 𝑢)
41, 3syl 17 1 (∀𝑥 𝑥 = 𝑦 → ∀𝑧𝑡 𝑡 = 𝑢)
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
This theorem depends on definitions:  df-bi 196  df-an 385  df-ex 1696
This theorem is referenced by:  hbaev  1972  aev2  1973
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