Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > axc11 | Structured version Visualization version GIF version |
Description: Show that ax-c11 33190 can be derived from ax-c11n 33191 in the form of axc11n 2295. Normally, axc11 2302 should be used rather than ax-c11 33190, 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 2175 | . 2 ⊢ (∀𝑦 𝑦 = 𝑥 → (∀𝑥𝜑 → ∀𝑦𝜑)) | |
2 | 1 | aecoms 2300 | 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-10 2006 ax-12 2034 ax-13 2234 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-tru 1478 df-ex 1696 df-nf 1701 |
This theorem is referenced by: hbae 2303 dral1 2313 dral1ALT 2314 nd1 9288 nd2 9289 axc11n11 31859 bj-hbaeb2 31993 wl-aetr 32496 ax6e2eq 37794 ax6e2eqVD 38165 2sb5ndVD 38168 2sb5ndALT 38190 |
Copyright terms: Public domain | W3C validator |