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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-axc11v | Structured version Visualization version GIF version |
Description: Version of axc11 2302 with a dv condition, which does not require ax-13 2234 nor ax-10 2006. Remark: the following theorems (hbae 2303, nfae 2304, hbnae 2305, nfnae 2306, hbnaes 2307) would need to be totally unbundled to be proved without ax-13 2234, hence would be simple consequences of ax-5 1827 or nfv 1830. (Contributed by BJ, 31-May-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-axc11v | ⊢ (∀𝑥 𝑥 = 𝑦 → (∀𝑥𝜑 → ∀𝑦𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | axc11r 2175 | . 2 ⊢ (∀𝑦 𝑦 = 𝑥 → (∀𝑥𝜑 → ∀𝑦𝜑)) | |
2 | 1 | bj-aecomsv 31934 | 1 ⊢ (∀𝑥 𝑥 = 𝑦 → (∀𝑥𝜑 → ∀𝑦𝜑)) |
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 ax-12 2034 |
This theorem depends on definitions: df-bi 196 df-an 385 df-ex 1696 |
This theorem is referenced by: bj-dral1v 31936 |
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