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Theorem mpbir3an 1085
Description: Detach a conjunction of truths in a biconditional. (Contributed by NM, 16-Sep-2011.) (Revised by NM, 9-Jan-2015.)
Hypotheses
Ref Expression
mpbir3an.1 ψ
mpbir3an.2 χ
mpbir3an.3 θ
mpbir3an.4 (φ ↔ (ψ χ θ))
Assertion
Ref Expression
mpbir3an φ

Proof of Theorem mpbir3an
StepHypRef Expression
1 mpbir3an.1 . . 3 ψ
2 mpbir3an.2 . . 3 χ
3 mpbir3an.3 . . 3 θ
41, 2, 33pm3.2i 1081 . 2 (ψ χ θ)
5 mpbir3an.4 . 2 (φ ↔ (ψ χ θ))
64, 5mpbir 134 1 φ
Colors of variables: wff set class
Syntax hints:  wb 98   w3a 884
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  df-3an 886
This theorem is referenced by:  limon  4204  limom  4279  issmo  5844  1eluzge0  8252  2eluzge0OLD  8254  2eluzge1  8255  0elunit  8584  1elunit  8585  4fvwrd4  8727  fzo0to42pr  8806
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