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Theorem hbanOLD 1829
 Description: Obsolete proof of hban 1828 as of 2-Jan-2018. (Contributed by NM, 5-Aug-1993.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
hb.1 (φxφ)
hb.2 (ψxψ)
Assertion
Ref Expression
hbanOLD ((φ ψ) → x(φ ψ))

Proof of Theorem hbanOLD
StepHypRef Expression
1 df-an 360 . 2 ((φ ψ) ↔ ¬ (φ → ¬ ψ))
2 hb.1 . . . 4 (φxφ)
3 hb.2 . . . . 5 (ψxψ)
43hbn 1776 . . . 4 ψx ¬ ψ)
52, 4hbim 1817 . . 3 ((φ → ¬ ψ) → x(φ → ¬ ψ))
65hbn 1776 . 2 (¬ (φ → ¬ ψ) → x ¬ (φ → ¬ ψ))
71, 6hbxfrbi 1568 1 ((φ ψ) → x(φ ψ))
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 358  ∀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  ax-6 1729  ax-11 1746 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-nf 1545 This theorem is referenced by: (None)
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