Theorem axc16 2270

Description: Proof of older axiom ax-c16 34650. (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 2269	1 ⊢ (∀𝑥 𝑥 = 𝑦 → (𝜑 → ∀𝑥𝜑))

Syntax hints:   → wi 4  ∀wal 1618

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1859  ax-4 1874  ax-5 1976  ax-6 2042  ax-7 2078  ax-12 2184

This theorem depends on definitions:  df-bi 197  df-an 385  df-ex 1842

This theorem is referenced by:  axc16nfOLD  2296  ax12vALT  2553  hbs1  2561  exists2  2688  bj-ax6elem1  32928  axc11n11r  32950  bj-axc16g16  32951