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Theorem selconj 32866
Description: An inference for selecting one of a list of conjuncts. (Contributed by Giovanni Mascellani, 23-May-2019.)
Hypothesis
Ref Expression
selconj.1 (𝜑 ↔ (𝜓𝜒))
Assertion
Ref Expression
selconj ((𝜂𝜑) ↔ (𝜓 ∧ (𝜂𝜒)))

Proof of Theorem selconj
StepHypRef Expression
1 selconj.1 . . 3 (𝜑 ↔ (𝜓𝜒))
21anbi2i 726 . 2 ((𝜂𝜑) ↔ (𝜂 ∧ (𝜓𝜒)))
3 an12 834 . 2 ((𝜓 ∧ (𝜂𝜒)) ↔ (𝜂 ∧ (𝜓𝜒)))
42, 3bitr4i 266 1 ((𝜂𝜑) ↔ (𝜓 ∧ (𝜂𝜒)))
Colors of variables: wff setvar class
Syntax hints:  wb 195  wa 383
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 196  df-an 385
This theorem is referenced by: (None)
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