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Theorem axc11 2206
Description: Show that ax-c11 33065 can be derived from ax-c11n 33066 in the form of axc11n 2199. Normally, axc11 2206 should be used rather than ax-c11 33065, 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 2136 . 2 (∀𝑦 𝑦 = 𝑥 → (∀𝑥𝜑 → ∀𝑦𝜑))
21aecoms 2204 1 (∀𝑥 𝑥 = 𝑦 → (∀𝑥𝜑 → ∀𝑦𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1472
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1700  ax-4 1713  ax-5 1793  ax-6 1838  ax-7 1885  ax-10 1966  ax-12 1983  ax-13 2137
This theorem depends on definitions:  df-bi 195  df-an 384  df-ex 1695  df-nf 1699
This theorem is referenced by:  hbae  2207  dral1  2217  dral1ALT  2218  nd1  9163  nd2  9164  axc11n11  31694  bj-hbaeb2  31835  wl-aetr  32370  ax6e2eq  37676  ax6e2eqVD  38047  2sb5ndVD  38050  2sb5ndALT  38072
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