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Theorem triantru3 35933
 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 535 . 2 ((𝜓𝜒) ↔ (𝜑 ∧ (𝜓𝜒)))
3 triantru3.2 . . 3 𝜓
43biantrur 535 . 2 (𝜒 ↔ (𝜓𝜒))
5 3anass 1093 . 2 ((𝜑𝜓𝜒) ↔ (𝜑 ∧ (𝜓𝜒)))
62, 4, 53bitr4i 307 1 (𝜒 ↔ (𝜑𝜓𝜒))
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 209   ∧ wa 400   ∧ w3a 1085 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 401  df-3an 1087 This theorem is referenced by:  eqvrelcoss  36285  eqvrelcoss3  36286
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