Theorem ax11f 2192

Description: Basis step for constructing a substitution instance of ax-11o 2141 without using ax-11o 2141. We can start with any formula ph in which x is not free. (Contributed by NM, 21-Jan-2007.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
ax11f.1	|- (ph -> A.xph)

Assertion

Ref	Expression
ax11f	|- (-. A.x x = y -> (x = y -> (ph -> A.x(x = y -> ph))))

Proof of Theorem ax11f

Step	Hyp	Ref	Expression
1		ax11f.1	. . 3 |- (ph -> A.xph)
2		ax-1 6	. . 3 |- (ph -> (x = y -> ph))
3	1, 2	alrimih 1565	. 2 |- (ph -> A.x(x = y -> ph))
4	3	2a1i 24	1 |- (-. A.x x = y -> (x = y -> (ph -> A.x(x = y -> ph))))

Syntax hints:  -. wn 3   -> wi 4  A.wal 1540

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-gen 1546  ax-5 1557

This theorem is referenced by: (None)