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Theorem pm5.4 248
Description: Antecedent absorption implication. Theorem *5.4 of [WhiteheadRussell] p. 125. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
pm5.4 ((𝜑 → (𝜑𝜓)) ↔ (𝜑𝜓))

Proof of Theorem pm5.4
StepHypRef Expression
1 pm2.43 53 . 2 ((𝜑 → (𝜑𝜓)) → (𝜑𝜓))
2 ax-1 6 . 2 ((𝜑𝜓) → (𝜑 → (𝜑𝜓)))
31, 2impbii 125 1 ((𝜑 → (𝜑𝜓)) ↔ (𝜑𝜓))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  sbequ8  1820  moabs  2049  rgenm  3468  isprm4  11829  limcdifap  12832
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