Theorem ax10w 2006

Description: Weak version of ax-10 2019 from which we can prove any ax-10 2019 instance not involving wff variables or bundling. Uses only Tarski's FOL axiom schemes. It is an alias of hbn1w 1973 introduced for labeling consistency. (Contributed by NM, 9-Apr-2017.) Use hbn1w 1973 instead. (New usage is discouraged.)

Hypothesis

Ref	Expression
ax10w.1	|- ( x = y -> ( ph <-> ps ) )

Assertion

Ref	Expression
ax10w	|- ( -. A. x ph -> A. x -. A. x ph )

Distinct variable groups:   ph, y   ps, x   x, y

Allowed substitution hints:   ph( x)   ps( y)

Proof of Theorem ax10w

Step	Hyp	Ref	Expression
1		ax10w.1	. 2 |- ( x = y -> ( ph <-> ps ) )
2	1	hbn1w 1973	1 |- ( -. A. x ph -> A. x -. A. x ph )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 196   A.wal 1481

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705

This theorem is referenced by: (None)