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Theorem axc11 2444
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.)
Assertion
Ref Expression
axc11 (∀𝑥 𝑥 = 𝑦 → (∀𝑥𝜑 → ∀𝑦𝜑))

Proof of Theorem axc11
StepHypRef Expression
1 axc11r 2377 . 2 (∀𝑦 𝑦 = 𝑥 → (∀𝑥𝜑 → ∀𝑦𝜑))
21aecoms 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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