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Theorem bi2.04 237
Description: Logical equivalence of commuted antecedents. Part of Theorem *4.87 of [WhiteheadRussell] p. 122. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
bi2.04 ((φ → (ψχ)) ↔ (ψ → (φχ)))

Proof of Theorem bi2.04
StepHypRef Expression
1 pm2.04 76 . 2 ((φ → (ψχ)) → (ψ → (φχ)))
2 pm2.04 76 . 2 ((ψ → (φχ)) → (φ → (ψχ)))
31, 2impbii 117 1 ((φ → (ψχ)) ↔ (ψ → (φχ)))
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:  imim21b  241  pm4.87  478  imimorbdc  779  sbcom2v  1834  mor  1915  r19.21t  2363  reu8  2705  ra5  2814  unissb  3573  reusv3  4130  tfi  4220  fun11  4880  prime  7901  bj-inf2vnlem2  8351
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