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Theorem hbbid 1464
Description: Deduction form of bound-variable hypothesis builder hbbi 1437. (Contributed by NM, 1-Jan-2002.)
Hypotheses
Ref Expression
hbbid.1 (φxφ)
hbbid.2 (φ → (ψxψ))
hbbid.3 (φ → (χxχ))
Assertion
Ref Expression
hbbid (φ → ((ψχ) → x(ψχ)))

Proof of Theorem hbbid
StepHypRef Expression
1 hbbid.1 . . . 4 (φxφ)
2 hbbid.2 . . . 4 (φ → (ψxψ))
3 hbbid.3 . . . 4 (φ → (χxχ))
41, 2, 3hbimd 1462 . . 3 (φ → ((ψχ) → x(ψχ)))
51, 3, 2hbimd 1462 . . 3 (φ → ((χψ) → x(χψ)))
64, 5anim12d 318 . 2 (φ → (((ψχ) (χψ)) → (x(ψχ) x(χψ))))
7 dfbi2 368 . 2 ((ψχ) ↔ ((ψχ) (χψ)))
8 albiim 1373 . 2 (x(ψχ) ↔ (x(ψχ) x(χψ)))
96, 7, 83imtr4g 194 1 (φ → ((ψχ) → x(ψχ)))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  wb 98  wal 1240
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-4 1397  ax-i5r 1425
This theorem depends on definitions:  df-bi 110
This theorem is referenced by: (None)
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