 New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  ax11wlem GIF version

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-1 5  ax-2 6  ax-3 7  ax-mp 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
 Copyright terms: Public domain W3C validator