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Theorem bianass 641
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 470 . 2 (((𝜂𝜓) ∧ 𝜒) ↔ (𝜂 ∧ (𝜓𝜒)))
42, 3bitr4i 278 1 ((𝜂𝜑) ↔ ((𝜂𝜓) ∧ 𝜒))
Colors of variables: wff setvar class
Syntax hints:  wb 205  wa 397
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 206  df-an 398
This theorem is referenced by:  bianassc  642  an12  644  an4  655  cnvresima  6230  elcncf1di  24411  nb3grpr2  28640  wwlksnextwrd  29151  cusgr3cyclex  34127  satfvsuclem2  34351  bj-prmoore  35996  bj-imdirco  36071  redundpim3  37500  isthincd2  47658
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