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Theorem axc16 2072
 Description: Proof of older axiom ax-c16 33070. (Contributed by NM, 8-Nov-2006.) (Revised by NM, 22-Sep-2017.)
Assertion
Ref Expression
axc16 (∀𝑥 𝑥 = 𝑦 → (𝜑 → ∀𝑥𝜑))
Distinct variable group:   𝑥,𝑦
Allowed substitution hints:   𝜑(𝑥,𝑦)

Proof of Theorem axc16
StepHypRef Expression
1 axc16g 2071 1 (∀𝑥 𝑥 = 𝑦 → (𝜑 → ∀𝑥𝜑))
 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-12 1983 This theorem depends on definitions:  df-bi 195  df-an 384  df-ex 1695 This theorem is referenced by:  axc16nf  2075  axc16nfOLD  2076  ax12vALT  2320  hbs1  2328  exists2  2454  bj-ax6elem1  31675  axc11n11r  31695  bj-axc16g16  31696  bj-ax12v  31794  bj-hbs1  31797
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