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Theorem triantru3 35381
Description: A wff is equivalent to its conjunctions with truths. (Contributed by Peter Mazsa, 30-Nov-2018.)
Hypotheses
Ref Expression
triantru3.1 𝜑
triantru3.2 𝜓
Assertion
Ref Expression
triantru3 (𝜒 ↔ (𝜑𝜓𝜒))

Proof of Theorem triantru3
StepHypRef Expression
1 triantru3.1 . . 3 𝜑
21biantrur 531 . 2 ((𝜓𝜒) ↔ (𝜑 ∧ (𝜓𝜒)))
3 triantru3.2 . . 3 𝜓
43biantrur 531 . 2 (𝜒 ↔ (𝜓𝜒))
5 3anass 1087 . 2 ((𝜑𝜓𝜒) ↔ (𝜑 ∧ (𝜓𝜒)))
62, 4, 53bitr4i 304 1 (𝜒 ↔ (𝜑𝜓𝜒))
Colors of variables: wff setvar class
Syntax hints:  wb 207  wa 396  w3a 1079
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 208  df-an 397  df-3an 1081
This theorem is referenced by:  eqvrelcoss  35732  eqvrelcoss3  35733
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