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Theorem dedlem0a 999
Description: Lemma for an alternate version of weak deduction theorem. (Contributed by NM, 2-Apr-1994.) (Proof shortened by Andrew Salmon, 7-May-2011.) (Proof shortened by Wolf Lammen, 4-Dec-2012.)
Assertion
Ref Expression
dedlem0a (𝜑 → (𝜓 ↔ ((𝜒𝜑) → (𝜓𝜑))))

Proof of Theorem dedlem0a
StepHypRef Expression
1 iba 524 . 2 (𝜑 → (𝜓 ↔ (𝜓𝜑)))
2 ax-1 6 . . 3 (𝜑 → (𝜒𝜑))
3 biimt 350 . . 3 ((𝜒𝜑) → ((𝜓𝜑) ↔ ((𝜒𝜑) → (𝜓𝜑))))
42, 3syl 17 . 2 (𝜑 → ((𝜓𝜑) ↔ ((𝜒𝜑) → (𝜓𝜑))))
51, 4bitrd 268 1 (𝜑 → (𝜓 ↔ ((𝜒𝜑) → (𝜓𝜑))))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  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-an 386
This theorem is referenced by:  iftrue  4070
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