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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 → (φψ))
Assertion
Ref Expression
ax11wlem (x = y → (φx(x = yφ)))
Distinct variable group:   ψ,x
Allowed substitution hints:   φ(x,y)   ψ(y)

Proof of Theorem ax11wlem
StepHypRef Expression
1 ax11wlemw.1 . 2 (x = y → (φψ))
2 ax-17 1616 . 2 (ψxψ)
31, 2ax11i 1647 1 (x = y → (φx(x = yφ)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176  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
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