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Mirrors > Home > MPE Home > Th. List > axc11 | Structured version Visualization version GIF version |
Description: Show that ax-c11 35903 can be derived from ax-c11n 35904 in the form of axc11n 2440. Normally, axc11 2444 should be used rather than ax-c11 35903, 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 2377 | . 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 1526 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-10 2136 ax-12 2167 ax-13 2381 |
This theorem depends on definitions: df-bi 208 df-an 397 df-ex 1772 df-nf 1776 |
This theorem is referenced by: hbae 2445 dral1 2453 dral1ALT 2454 nd1 9997 nd2 9998 axc11n11 33913 bj-hbaeb2 34038 wl-aetr 34651 ax6e2eq 40768 ax6e2eqVD 41118 2sb5ndVD 41121 2sb5ndALT 41143 |
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