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Theorem dedth3v 3708
 Description: Weak deduction theorem for eliminating a hypothesis with 3 class variables. See comments in dedth2v 3707. (Contributed by NM, 13-Aug-1999.) (Proof shortened by Eric Schmidt, 28-Jul-2009.)
Hypotheses
Ref Expression
dedth3v.1 (A = if(φ, A, D) → (ψχ))
dedth3v.2 (B = if(φ, B, R) → (χθ))
dedth3v.3 (C = if(φ, C, S) → (θτ))
dedth3v.4 τ
Assertion
Ref Expression
dedth3v (φψ)

Proof of Theorem dedth3v
StepHypRef Expression
1 dedth3v.1 . . . 4 (A = if(φ, A, D) → (ψχ))
2 dedth3v.2 . . . 4 (B = if(φ, B, R) → (χθ))
3 dedth3v.3 . . . 4 (C = if(φ, C, S) → (θτ))
4 dedth3v.4 . . . 4 τ
51, 2, 3, 4dedth3h 3705 . . 3 ((φ φ φ) → ψ)
653anidm12 1239 . 2 ((φ φ) → ψ)
76anidms 626 1 (φψ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176   = wceq 1642   ifcif 3662 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-if 3663 This theorem is referenced by: (None)
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