Theorem ax16 2045

Description: Proof of older axiom ax-16 2144. (Contributed by NM, 8-Nov-2006.) (Revised by NM, 22-Sep-2017.)

Assertion

Ref	Expression
ax16	⊢ (∀x x = y → (φ → ∀xφ))

Distinct variable group:   x,y

Allowed substitution hints:   φ(x,y)

Proof of Theorem ax16

Step	Hyp	Ref	Expression
1		a16g 1945	1 ⊢ (∀x x = y → (φ → ∀xφ))

Syntax hints:   → wi 4  ∀wal 1540

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925

This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545

This theorem is referenced by:  ax11v  2096  hbs1  2105  exists2  2294