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Theorem axc11 2456
Description: Show that ax-c11 34694 can be derived from ax-c11n 34695 in the form of axc11n 2451. Normally, axc11 2456 should be used rather than ax-c11 34694, 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 2332 . 2 (∀𝑦 𝑦 = 𝑥 → (∀𝑥𝜑 → ∀𝑦𝜑))
21aecoms 2454 1 (∀𝑥 𝑥 = 𝑦 → (∀𝑥𝜑 → ∀𝑦𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1630
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-10 2168  ax-12 2196  ax-13 2391
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-ex 1854  df-nf 1859
This theorem is referenced by:  hbae  2457  dral1  2465  dral1ALT  2466  nd1  9621  nd2  9622  axc11n11  33000  bj-hbaeb2  33133  wl-aetr  33648  ax6e2eq  39293  ax6e2eqVD  39660  2sb5ndVD  39663  2sb5ndALT  39685
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