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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 ↔ (𝜒𝜓)))

Proof of Theorem biantrud
StepHypRef Expression
1 biantrud.1 . 2 (𝜑𝜓)
2 iba 284 . 2 (𝜓 → (𝜒 ↔ (𝜒𝜓)))
31, 2syl 14 1 (𝜑 → (𝜒 ↔ (𝜒𝜓)))
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  4412  elrnmpt1  4585  fliftf  5439  elxp7  5797  eroveu  6197  reapltxor  7580  divap0b  7662  nnle1eq1  7938  nn0le0eq0  8210  nn0lt10b  8321  ioopos  8819
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