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Mirrors > Home > MPE Home > Th. List > axc11 | Structured version Visualization version GIF version |
Description: Show that ax-c11 34645 can be derived from ax-c11n 34646 in the form of axc11n 2439. Normally, axc11 2444 should be used rather than ax-c11 34645, except by theorems specifically studying the latter's properties. (Contributed by NM, 16-May-2008.) (Proof shortened by Wolf Lammen, 21-Apr-2018.) |
Ref | Expression |
---|---|
axc11 | ⊢ (∀𝑥 𝑥 = 𝑦 → (∀𝑥𝜑 → ∀𝑦𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | axc11r 2320 | . 2 ⊢ (∀𝑦 𝑦 = 𝑥 → (∀𝑥𝜑 → ∀𝑦𝜑)) | |
2 | 1 | aecoms 2442 | 1 ⊢ (∀𝑥 𝑥 = 𝑦 → (∀𝑥𝜑 → ∀𝑦𝜑)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1618 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1859 ax-4 1874 ax-5 1976 ax-6 2042 ax-7 2078 ax-10 2156 ax-12 2184 ax-13 2379 |
This theorem depends on definitions: df-bi 197 df-or 384 df-an 385 df-ex 1842 df-nf 1847 |
This theorem is referenced by: hbae 2445 dral1 2453 dral1ALT 2454 nd1 9572 nd2 9573 axc11n11 32949 bj-hbaeb2 33082 wl-aetr 33599 ax6e2eq 39244 ax6e2eqVD 39611 2sb5ndVD 39614 2sb5ndALT 39636 |
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