Theorem axc11 2396

Description: Show that ax-c11 35041 can be derived from ax-c11n 35042 in the form of axc11n 2392. Normally, axc11 2396 should be used rather than ax-c11 35041, 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

Step	Hyp	Ref	Expression
1		axc11r 2333	. 2 ⊢ (∀𝑦 𝑦 = 𝑥 → (∀𝑥𝜑 → ∀𝑦𝜑))
2	1	aecoms 2394	1 ⊢ (∀𝑥 𝑥 = 𝑦 → (∀𝑥𝜑 → ∀𝑦𝜑))

Syntax hints:   → wi 4  ∀wal 1599

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1839  ax-4 1853  ax-5 1953  ax-6 2021  ax-7 2055  ax-10 2135  ax-12 2163  ax-13 2334

This theorem depends on definitions:  df-bi 199  df-an 387  df-ex 1824  df-nf 1828

This theorem is referenced by:  hbae  2397  dral1  2405  dral1ALT  2406  nd1  9744  nd2  9745  axc11n11  33261  bj-hbaeb2  33380  wl-aetr  33911  ax6e2eq  39717  ax6e2eqVD  40076  2sb5ndVD  40079  2sb5ndALT  40101