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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-axc11v | Structured version Visualization version GIF version |
Description: Version of axc11 2430 with a disjoint variable condition, which does not require ax-13 2372 nor ax-10 2138. Remark: the following theorems (hbae 2431, nfae 2433, hbnae 2432, nfnae 2434, hbnaes 2435) would need to be totally unbundled to be proved without ax-13 2372, hence would be simple consequences of ax-5 1914 or nfv 1918. (Contributed by BJ, 31-May-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-axc11v | ⊢ (∀𝑥 𝑥 = 𝑦 → (∀𝑥𝜑 → ∀𝑦𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | axc11rv 2257 | . 2 ⊢ (∀𝑦 𝑦 = 𝑥 → (∀𝑥𝜑 → ∀𝑦𝜑)) | |
2 | 1 | bj-aecomsv 35686 | 1 ⊢ (∀𝑥 𝑥 = 𝑦 → (∀𝑥𝜑 → ∀𝑦𝜑)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1540 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-12 2172 |
This theorem depends on definitions: df-bi 206 df-an 398 df-ex 1783 |
This theorem is referenced by: (None) |
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