Theorem axc16 2299

Description: Proof of older axiom ax-c16 39724. (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 2298	1 ⊢ (∀𝑥 𝑥 = 𝑦 → (𝜑 → ∀𝑥𝜑))

This proof depends on syntax axioms:   → wi 4  ∀wal 1568

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-12 2216

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1813

This theorem is used by:  axc11rv  2303  ax12vALT  2503  bj-ax6elem1  37345  axc11n11r  37365  bj-axc16g16  37366