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Theorem 3pm3.2i 1130
Description: Infer conjunction of premises. (Contributed by NM, 10-Feb-1995.)
Hypotheses
Ref Expression
3pm3.2i.1 φ
3pm3.2i.2 ψ
3pm3.2i.3 χ
Assertion
Ref Expression
3pm3.2i (φ ψ χ)

Proof of Theorem 3pm3.2i
StepHypRef Expression
1 3pm3.2i.1 . . 3 φ
2 3pm3.2i.2 . . 3 ψ
31, 2pm3.2i 441 . 2 (φ ψ)
4 3pm3.2i.3 . 2 χ
5 df-3an 936 . 2 ((φ ψ χ) ↔ ((φ ψ) χ))
63, 4, 5mpbir2an 886 1 (φ ψ χ)
Colors of variables: wff setvar class
Syntax hints:   wa 358   w3a 934
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936
This theorem is referenced by:  mpbir3an  1134  3jaoi  1245
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