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Mirrors > Home > MPE Home > Th. List > axc11 | Structured version Visualization version GIF version |
Description: Show that ax-c11 38868 can be derived from ax-c11n 38869 in the form of axc11n 2428. Normally, axc11 2432 should be used rather than ax-c11 38868, except by theorems specifically studying the latter's properties. Usage of this theorem is discouraged because it depends on ax-13 2374. Use the weaker axc11v 2261 when possible. (Contributed by NM, 16-May-2008.) (Proof shortened by Wolf Lammen, 21-Apr-2018.) (New usage is discouraged.) |
Ref | Expression |
---|---|
axc11 | ⊢ (∀𝑥 𝑥 = 𝑦 → (∀𝑥𝜑 → ∀𝑦𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | axc11r 2368 | . 2 ⊢ (∀𝑦 𝑦 = 𝑥 → (∀𝑥𝜑 → ∀𝑦𝜑)) | |
2 | 1 | aecoms 2430 | 1 ⊢ (∀𝑥 𝑥 = 𝑦 → (∀𝑥𝜑 → ∀𝑦𝜑)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1534 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1791 ax-4 1805 ax-5 1907 ax-6 1964 ax-7 2004 ax-10 2138 ax-12 2174 ax-13 2374 |
This theorem depends on definitions: df-bi 207 df-an 396 df-ex 1776 df-nf 1780 |
This theorem is referenced by: hbae 2433 dral1 2441 dral1ALT 2442 nd1 10624 nd2 10625 axc11n11 36664 bj-hbaeb2 36800 wl-aetr 37509 ax6e2eq 44554 ax6e2eqVD 44904 2sb5ndVD 44907 2sb5ndALT 44929 |
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