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Theorem axc11 2197
Description: Show that ax-c11 32692 can be derived from ax-c11n 32693 in the form of axc11n 2191. Normally, axc11 2197 should be used rather than ax-c11 32692, 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 2073 . 2 (∀𝑦 𝑦 = 𝑥 → (∀𝑥𝜑 → ∀𝑦𝜑))
21aecoms 2195 1 (∀𝑥 𝑥 = 𝑦 → (∀𝑥𝜑 → ∀𝑦𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1466
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1698  ax-4 1711  ax-5 1789  ax-6 1836  ax-7 1883  ax-10 1965  ax-12 1983  ax-13 2137
This theorem depends on definitions:  df-bi 192  df-an 380  df-ex 1693  df-nf 1697
This theorem is referenced by:  hbae  2198  dral1  2208  dral1ALT  2209  nd1  9097  nd2  9098  bj-hbaeb2  31602  wl-aetr  32094  ax6e2eq  37280  ax6e2eqVD  37652  2sb5ndVD  37655  2sb5ndALT  37677
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