Theorem ax11dgen 1722

Description: Degenerate instance of ax-11 1746 where bundled variables x and y have a common substitution. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 13-Apr-2017.)

Assertion

Ref	Expression
ax11dgen	|- (x = x -> (A.xph -> A.x(x = x -> ph)))

Proof of Theorem ax11dgen

Step	Hyp	Ref	Expression
1		ax-1 6	. . 3 |- (ph -> (x = x -> ph))
2	1	alimi 1559	. 2 |- (A.xph -> A.x(x = x -> ph))
3	2	a1i 10	1 |- (x = x -> (A.xph -> A.x(x = x -> ph)))

This proof depends on syntax axioms:   -> wi 4  A.wal 1540

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-gen 1546  ax-5 1557

This theorem is used by: (None)