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Theorem 2th 163
Description: Two truths are equivalent. (Contributed by NM, 18-Aug-1993.)
Hypotheses
Ref Expression
2th.1 φ
2th.2 ψ
Assertion
Ref Expression
2th (φψ)

Proof of Theorem 2th
StepHypRef Expression
1 2th.2 . . 3 ψ
21a1i 9 . 2 (φψ)
3 2th.1 . . 3 φ
43a1i 9 . 2 (ψφ)
52, 4impbii 117 1 (φψ)
Colors of variables: wff set class
Syntax hints:  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:  trujust  1244  dftru2  1250  bitru  1254  vjust  2552  pwv  3570  int0  3620  0iin  3706  snnex  4147  ruv  4228  fo1st  5726  fo2nd  5727  eqer  6074  ener  6195  bdth  9286
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