NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  biantrud GIF version

Theorem biantrud 493
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 489 . 2 (ψ → (χ ↔ (χ ψ)))
31, 2syl 15 1 (φ → (χ ↔ (χ ψ)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176   wa 358
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 177  df-an 360
This theorem is referenced by:  ssofss  4076  eqtfinrelk  4486  ovmpt2x  5712  clos1induct  5880
  Copyright terms: Public domain W3C validator