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Theorem an12i 32853
Description: An inference from commuting operands in a chain of conjunctions. (Contributed by Giovanni Mascellani, 22-May-2019.)
Hypothesis
Ref Expression
an12i.1 (𝜑 ∧ (𝜓𝜒))
Assertion
Ref Expression
an12i (𝜓 ∧ (𝜑𝜒))

Proof of Theorem an12i
StepHypRef Expression
1 an12i.1 . 2 (𝜑 ∧ (𝜓𝜒))
2 an12 833 . 2 ((𝜓 ∧ (𝜑𝜒)) ↔ (𝜑 ∧ (𝜓𝜒)))
31, 2mpbir 219 1 (𝜓 ∧ (𝜑𝜒))
Colors of variables: wff setvar class
Syntax hints:  wa 382
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 195  df-an 384
This theorem is referenced by: (None)
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