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Theorem biantrud 288
 Description: A wff is equivalent to its conjunction with truth. (Contributed by NM, 2-Aug-1994.) (Proof shortened by Wolf Lammen, 23-Oct-2013.)
Hypothesis
Ref Expression
biantrud.1 (φψ)
Assertion
Ref Expression
biantrud (φ → (χ ↔ (χ ψ)))

Proof of Theorem biantrud
StepHypRef Expression
1 biantrud.1 . 2 (φψ)
2 iba 284 . 2 (ψ → (χ ↔ (χ ψ)))
31, 2syl 14 1 (φ → (χ ↔ (χ ψ)))
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 97   ↔ wb 98 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101 This theorem depends on definitions:  df-bi 110 This theorem is referenced by:  posng  4355  elrnmpt1  4528  fliftf  5382  elxp7  5739  eroveu  6133  reapltxor  7373  divap0b  7444  nnle1eq1  7719  nn0le0eq0  7986  nn0lt10b  8097  ioopos  8589
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