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Theorem hbaevg 1981
 Description: Generalization of hbaev 1982, proved at no extra cost. Instance of aev2 1983. (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 1978 . 2 (∀𝑥 𝑥 = 𝑦 → ∀𝑣 𝑣 = 𝑤)
2 aevlem 1978 . . 3 (∀𝑣 𝑣 = 𝑤 → ∀𝑡 𝑡 = 𝑢)
32alrimiv 1852 . 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 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 This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1702 This theorem is referenced by:  hbaev  1982  aev2  1983
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