Theorem ax13w 2013

Description: Weak version (principal instance) of ax-13 2246. (Because y and z don't need to be distinct, this actually bundles the principal instance and the degenerate instance ( -. x = y -> ( y = y -> A. x y = y ) ).) Uses only Tarski's FOL axiom schemes. The proof is trivial but is included to complete the set ax10w 2006, ax11w 2007, and ax12w 2010. (Contributed by NM, 10-Apr-2017.)

Assertion

Ref	Expression
ax13w	|- ( -. x = y -> ( y = z -> A. x y = z ) )

Distinct variable groups:   x, y   x, z

Proof of Theorem ax13w

Step	Hyp	Ref	Expression
1		ax5d 1840	1 |- ( -. x = y -> ( y = z -> A. x y = z ) )

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

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-5 1839

This theorem is referenced by: (None)