Theorem axc16 2299

Description: Proof of older axiom ax-c16 39523. (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))

Syntax hints:   → wi 4  ∀wal 1561

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1818  ax-4 1832  ax-5 1933  ax-6 1990  ax-7 2031  ax-12 2215

This theorem depends on definitions:  df-bi 210  df-an 401  df-ex 1803

This theorem is referenced by:  axc11rv  2303  ax12vALT  2503  bj-ax6elem1  37145  axc11n11r  37165  bj-axc16g16  37166