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Theorem pm5.21nd 836
Description: Eliminate an antecedent implied by each side of a biconditional. (The proof was 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 107 . 2
3 pm5.21nd.2 . . 3
43ex 107 . 2
5 pm5.21nd.3 . . 3
65a1i 10 . 2
72, 4, 6pm5.21ndd 600 1
Colors of variables: wff set class
Syntax hints:   wi 4   wa 96   wb 97
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8  ax-ia1 98  ax-ia2 99  ax-ia3 100
This theorem depends on definitions:  df-bi 109
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