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Theorem bj-axc11v 36792
Description: Version of axc11 2433 with a disjoint variable condition, which does not require ax-13 2375 nor ax-10 2139. Remark: the following theorems (hbae 2434, nfae 2436, hbnae 2435, nfnae 2437, hbnaes 2438) would need to be totally unbundled to be proved without ax-13 2375, hence would be simple consequences of ax-5 1908 or nfv 1912. (Contributed by BJ, 31-May-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-axc11v (∀𝑥 𝑥 = 𝑦 → (∀𝑥𝜑 → ∀𝑦𝜑))
Distinct variable group:   𝑥,𝑦
Allowed substitution hints:   𝜑(𝑥,𝑦)

Proof of Theorem bj-axc11v
StepHypRef Expression
1 axc11rv 2263 . 2 (∀𝑦 𝑦 = 𝑥 → (∀𝑥𝜑 → ∀𝑦𝜑))
21bj-aecomsv 36791 1 (∀𝑥 𝑥 = 𝑦 → (∀𝑥𝜑 → ∀𝑦𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1535
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-12 2175
This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1777
This theorem is referenced by: (None)
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