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Theorem biantrurd 494
 Description: A wff is equivalent to its conjunction with truth. (Contributed by NM, 1-May-1995.) (Proof shortened by Andrew Salmon, 7-May-2011.)
Hypothesis
Ref Expression
biantrud.1 (φψ)
Assertion
Ref Expression
biantrurd (φ → (χ ↔ (ψ χ)))

Proof of Theorem biantrurd
StepHypRef Expression
1 biantrud.1 . 2 (φψ)
2 ibar 490 . 2 (ψ → (χ ↔ (ψ χ)))
31, 2syl 15 1 (φ → (χ ↔ (ψ χ)))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176   ∧ wa 358 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8 This theorem depends on definitions:  df-bi 177  df-an 360 This theorem is referenced by:  3anibar  1123  n0moeu  3562  opkelcokg  4261  opkelimagekg  4271  reiota2  4368  opbrop  4841  funcnv3  5157  fnssresb  5195  dff1o5  5295  dffo3  5422  fconst4  5458  eloprabga  5578  nenpw1pwlem2  6085
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