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Theorem frege55lem1a 38942
 Description: Necessary deduction regarding substitution of value in equality. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege55lem1a ((𝜏 → if-(𝜓, 𝜑, ¬ 𝜑)) → (𝜏 → (𝜓𝜑)))

Proof of Theorem frege55lem1a
StepHypRef Expression
1 frege54cor0a 38939 . . 3 ((𝜓𝜑) ↔ if-(𝜓, 𝜑, ¬ 𝜑))
21biimpri 220 . 2 (if-(𝜓, 𝜑, ¬ 𝜑) → (𝜓𝜑))
32imim2i 16 1 ((𝜏 → if-(𝜓, 𝜑, ¬ 𝜑)) → (𝜏 → (𝜓𝜑)))
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 198  if-wif 1086 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-frege28 38906 This theorem depends on definitions:  df-bi 199  df-an 386  df-or 875  df-ifp 1087 This theorem is referenced by:  frege55cor1a  38945
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