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Theorem bianass 640
Description: An inference to merge two lists of conjuncts. (Contributed by Giovanni Mascellani, 23-May-2019.)
Hypothesis
Ref Expression
bianass.1 (𝜑 ↔ (𝜓𝜒))
Assertion
Ref Expression
bianass ((𝜂𝜑) ↔ ((𝜂𝜓) ∧ 𝜒))

Proof of Theorem bianass
StepHypRef Expression
1 bianass.1 . . 3 (𝜑 ↔ (𝜓𝜒))
21anbi2i 624 . 2 ((𝜂𝜑) ↔ (𝜂 ∧ (𝜓𝜒)))
3 anass 471 . 2 (((𝜂𝜓) ∧ 𝜒) ↔ (𝜂 ∧ (𝜓𝜒)))
42, 3bitr4i 280 1 ((𝜂𝜑) ↔ ((𝜂𝜓) ∧ 𝜒))
Colors of variables: wff setvar class
Syntax hints:  wb 208  wa 398
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 209  df-an 399
This theorem is referenced by:  bianassc  641  an12  643  an4  654  cnvresima  6082  elcncf1di  23497  nb3grpr2  27159  wwlksnextwrd  27669  cusgr3cyclex  32378  satfvsuclem2  32602  etasslt  33269  bj-prmoore  34401  redundpim3  35859
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