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Theorem axc16 2076
Description: Proof of older axiom ax-c16 32697. (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 2075 1 (∀𝑥 𝑥 = 𝑦 → (𝜑 → ∀𝑥𝜑))
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-12 1983
This theorem depends on definitions:  df-bi 192  df-an 380  df-ex 1693
This theorem is referenced by:  axc16nf  2079  ax12vALT  2311  hbs1  2319  exists2  2445  bj-ax6elem1  31446  bj-ax12v  31561  bj-hbs1  31564
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