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Theorem hbn1w 1706
 Description: Weak version of hbn1 1730. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 9-Apr-2017.)
Hypothesis
Ref Expression
hbn1w.1 (x = y → (φψ))
Assertion
Ref Expression
hbn1w xφx ¬ xφ)
Distinct variable groups:   φ,y   ψ,x   x,y
Allowed substitution hints:   φ(x)   ψ(y)

Proof of Theorem hbn1w
StepHypRef Expression
1 ax-17 1616 . 2 (xφyxφ)
2 ax-17 1616 . 2 ψx ¬ ψ)
3 ax-17 1616 . 2 (yψxyψ)
4 ax-17 1616 . 2 φy ¬ φ)
5 ax-17 1616 . 2 yψx ¬ yψ)
6 hbn1w.1 . 2 (x = y → (φψ))
71, 2, 3, 4, 5, 6hbn1fw 1705 1 xφx ¬ xφ)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → 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  ax-9 1654  ax-8 1675 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542 This theorem is referenced by:  hba1w  1707  hbe1w  1708  ax6w  1717
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