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Theorem ax11i 1647
 Description: Inference that has ax-11 1746 (without ∀y) as its conclusion. Uses only Tarski's FOL axiom schemes. The hypotheses may be eliminable without one or more of these axioms in special cases. Proof similar to Lemma 16 of [Tarski] p. 70. (Contributed by NM, 20-May-2008.)
Hypotheses
Ref Expression
ax11i.1 (x = y → (φψ))
ax11i.2 (ψxψ)
Assertion
Ref Expression
ax11i (x = y → (φx(x = yφ)))

Proof of Theorem ax11i
StepHypRef Expression
1 ax11i.1 . 2 (x = y → (φψ))
2 ax11i.2 . . 3 (ψxψ)
31biimprcd 216 . . 3 (ψ → (x = yφ))
42, 3alrimih 1565 . 2 (ψx(x = yφ))
51, 4syl6bi 219 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 This theorem depends on definitions:  df-bi 177 This theorem is referenced by:  ax11wlem  1720
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