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

Step	Hyp	Ref	Expression
1		axc16g 2075	1 ⊢ (∀𝑥 𝑥 = 𝑦 → (𝜑 → ∀𝑥𝜑))

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