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Theorem pm5.21nd 787
Description: Eliminate an antecedent implied by each side of a biconditional. (Contributed by NM, 20-Nov-2005.) (Proof shortened by Wolf Lammen, 4-Nov-2013.)
Hypotheses
Ref Expression
pm5.21nd.1
pm5.21nd.2
pm5.21nd.3
Assertion
Ref Expression
pm5.21nd

Proof of Theorem pm5.21nd
StepHypRef Expression
1 pm5.21nd.1 . . 3
21ex 106 . 2
3 pm5.21nd.2 . . 3
43ex 106 . 2
5 pm5.21nd.3 . . 3
65a1i 9 . 2
72, 4, 6pm5.21ndd 602 1
Colors of variables: wff set class
Syntax hints:   wi 4   wa 95   wb 96
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 97  ax-ia2 98  ax-ia3 99
This theorem depends on definitions:  df-bi 108
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