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Theorem elimhOLD 1032
Description: Old version of elimh 1029. Obsolete as of 16-Mar-2021. (Contributed by NM, 26-Jun-2002.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
elimhOLD.1 ((𝜑 ↔ ((𝜑𝜒) ∨ (𝜓 ∧ ¬ 𝜒))) → (𝜒𝜏))
elimhOLD.2 ((𝜓 ↔ ((𝜑𝜒) ∨ (𝜓 ∧ ¬ 𝜒))) → (𝜃𝜏))
elimhOLD.3 𝜃
Assertion
Ref Expression
elimhOLD 𝜏

Proof of Theorem elimhOLD
StepHypRef Expression
1 dedlema 1001 . . . 4 (𝜒 → (𝜑 ↔ ((𝜑𝜒) ∨ (𝜓 ∧ ¬ 𝜒))))
2 elimhOLD.1 . . . 4 ((𝜑 ↔ ((𝜑𝜒) ∨ (𝜓 ∧ ¬ 𝜒))) → (𝜒𝜏))
31, 2syl 17 . . 3 (𝜒 → (𝜒𝜏))
43ibi 256 . 2 (𝜒𝜏)
5 elimhOLD.3 . . 3 𝜃
6 dedlemb 1002 . . . 4 𝜒 → (𝜓 ↔ ((𝜑𝜒) ∨ (𝜓 ∧ ¬ 𝜒))))
7 elimhOLD.2 . . . 4 ((𝜓 ↔ ((𝜑𝜒) ∨ (𝜓 ∧ ¬ 𝜒))) → (𝜃𝜏))
86, 7syl 17 . . 3 𝜒 → (𝜃𝜏))
95, 8mpbii 223 . 2 𝜒𝜏)
104, 9pm2.61i 176 1 𝜏
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 196  wo 383  wa 384
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386
This theorem is referenced by:  con3OLD  1034
  Copyright terms: Public domain W3C validator