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Theorem ibibr 235
Description: Implication in terms of implication and biconditional. (Contributed by NM, 29-Apr-2005.) (Proof shortened by Wolf Lammen, 21-Dec-2013.)
Assertion
Ref Expression
ibibr ((φψ) ↔ (φ → (ψφ)))

Proof of Theorem ibibr
StepHypRef Expression
1 pm5.501 233 . . 3 (φ → (ψ ↔ (φψ)))
2 bicom 128 . . 3 ((φψ) ↔ (ψφ))
31, 2syl6bb 185 . 2 (φ → (ψ ↔ (ψφ)))
43pm5.74i 169 1 ((φψ) ↔ (φ → (ψφ)))
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-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  tbt  236  oibabs  799  rabxfrd  4167
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