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Theorem pm5.4 238
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 47 . 2 ((φ → (φψ)) → (φψ))
2 ax-1 5 . 2 ((φψ) → (φ → (φψ)))
31, 2impbii 117 1 ((φ → (φψ)) ↔ (φψ))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  sbequ8  1724  moabs  1946  rgenm  3317
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