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Theorem bianassc 642
Description: An inference to merge two lists of conjuncts. (Contributed by Peter Mazsa, 24-Sep-2022.)
Hypothesis
Ref Expression
bianass.1 (𝜑 ↔ (𝜓𝜒))
Assertion
Ref Expression
bianassc ((𝜂𝜑) ↔ ((𝜓𝜂) ∧ 𝜒))

Proof of Theorem bianassc
StepHypRef Expression
1 bianass.1 . . 3 (𝜑 ↔ (𝜓𝜒))
21bianass 641 . 2 ((𝜂𝜑) ↔ ((𝜂𝜓) ∧ 𝜒))
3 ancom 464 . . 3 ((𝜂𝜓) ↔ (𝜓𝜂))
43anbi1i 626 . 2 (((𝜂𝜓) ∧ 𝜒) ↔ ((𝜓𝜂) ∧ 𝜒))
52, 4bitri 278 1 ((𝜂𝜑) ↔ ((𝜓𝜂) ∧ 𝜒))
Colors of variables: wff setvar class
Syntax hints:  wb 209  wa 399
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 210  df-an 400
This theorem is referenced by:  an21  643  ssrnres  6002  fvmptnn04if  21454  bj-restuni  34509
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