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Theorem hb3and 1376
Description: Deduction form of bound-variable hypothesis builder hb3an 1439. (Contributed by NM, 17-Feb-2013.)
Hypotheses
Ref Expression
hb3and.1 (φ → (ψxψ))
hb3and.2 (φ → (χxχ))
hb3and.3 (φ → (θxθ))
Assertion
Ref Expression
hb3and (φ → ((ψ χ θ) → x(ψ χ θ)))

Proof of Theorem hb3and
StepHypRef Expression
1 hb3and.1 . . 3 (φ → (ψxψ))
2 hb3and.2 . . 3 (φ → (χxχ))
3 hb3and.3 . . 3 (φ → (θxθ))
41, 2, 33anim123d 1213 . 2 (φ → ((ψ χ θ) → (xψ xχ xθ)))
5 19.26-3an 1369 . 2 (x(ψ χ θ) ↔ (xψ xχ xθ))
64, 5syl6ibr 151 1 (φ → ((ψ χ θ) → x(ψ χ θ)))
Colors of variables: wff set class
Syntax hints:  wi 4   w3a 884  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
This theorem depends on definitions:  df-bi 110  df-3an 886
This theorem is referenced by: (None)
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