Theorem ax11wlem 1720

Description: Lemma for weak version of ax-11 1746. Uses only Tarski's FOL axiom schemes. In some cases, this lemma may lead to shorter proofs than ax11w 1721. (Contributed by NM, 10-Apr-2017.)

Hypothesis

Ref	Expression
ax11wlemw.1	|- (x = y -> (ph <-> ps))

Assertion

Ref	Expression
ax11wlem	|- (x = y -> (ph -> A.x(x = y -> ph)))

Distinct variable group:   ps,x

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

Proof of Theorem ax11wlem

Step	Hyp	Ref	Expression
1		ax11wlemw.1	. 2 |- (x = y -> (ph <-> ps))
2		ax-17 1616	. 2 |- (ps -> A.xps)
3	1, 2	ax11i 1647	1 |- (x = y -> (ph -> A.x(x = y -> ph)))

Syntax hints:   -> wi 4   <-> wb 176  A.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

This theorem depends on definitions:  df-bi 177

This theorem is referenced by:  ax11w  1721