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Theorem axc11 2313
Description: Show that ax-c11 33649 can be derived from ax-c11n 33650 in the form of axc11n 2306. Normally, axc11 2313 should be used rather than ax-c11 33649, 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 2186 . 2 (∀𝑦 𝑦 = 𝑥 → (∀𝑥𝜑 → ∀𝑦𝜑))
21aecoms 2311 1 (∀𝑥 𝑥 = 𝑦 → (∀𝑥𝜑 → ∀𝑦𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1478
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-10 2016  ax-12 2044  ax-13 2245
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ex 1702  df-nf 1707
This theorem is referenced by:  hbae  2314  dral1  2324  dral1ALT  2325  nd1  9353  nd2  9354  axc11n11  32311  bj-hbaeb2  32445  wl-aetr  32946  ax6e2eq  38252  ax6e2eqVD  38623  2sb5ndVD  38626  2sb5ndALT  38648
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