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Theorem axc11 2466
Description: Show that ax-c11 34688 can be derived from ax-c11n 34689 in the form of axc11n 2462. Normally, axc11 2466 should be used rather than ax-c11 34688, 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 2349 . 2 (∀𝑦 𝑦 = 𝑥 → (∀𝑥𝜑 → ∀𝑦𝜑))
21aecoms 2464 1 (∀𝑥 𝑥 = 𝑦 → (∀𝑥𝜑 → ∀𝑦𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1629
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-10 2174  ax-12 2203  ax-13 2408
This theorem depends on definitions:  df-bi 197  df-an 383  df-ex 1853  df-nf 1858
This theorem is referenced by:  hbae  2467  dral1  2475  dral1ALT  2476  nd1  9609  nd2  9610  axc11n11  33002  bj-hbaeb2  33133  wl-aetr  33645  ax6e2eq  39291  ax6e2eqVD  39658  2sb5ndVD  39661  2sb5ndALT  39683
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