New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  hb3anOLD GIF version

Theorem hb3anOLD 1831
 Description: Obsolete proof of hb3an 1830 as of 2-Jan-2018. (Contributed by NM, 14-Sep-2003.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
hb.1 (φxφ)
hb.2 (ψxψ)
hb.3 (χxχ)
Assertion
Ref Expression
hb3anOLD ((φ ψ χ) → x(φ ψ χ))

Proof of Theorem hb3anOLD
StepHypRef Expression
1 df-3an 936 . 2 ((φ ψ χ) ↔ ((φ ψ) χ))
2 hb.1 . . . 4 (φxφ)
3 hb.2 . . . 4 (ψxψ)
42, 3hban 1828 . . 3 ((φ ψ) → x(φ ψ))
5 hb.3 . . 3 (χxχ)
64, 5hban 1828 . 2 (((φ ψ) χ) → x((φ ψ) χ))
71, 6hbxfrbi 1568 1 ((φ ψ χ) → x(φ ψ χ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 358   ∧ w3a 934  ∀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-3an 936  df-tru 1319  df-ex 1542  df-nf 1545 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator