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Theorem axc16 2119
Description: Proof of older axiom ax-c16 32991. (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 2118 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 1712  ax-4 1727  ax-5 1826  ax-6 1874  ax-7 1921  ax-12 2033
This theorem depends on definitions:  df-bi 195  df-an 384  df-ex 1695
This theorem is referenced by:  axc16nfOLD  2148  ax12vALT  2415  hbs1  2423  exists2  2549  bj-ax6elem1  31646  axc11n11r  31666  bj-axc16g16  31667
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