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Theorem nanbi2 1296
Description: Introduce a left anti-conjunct to both sides of a logical equivalence. (Contributed by SF, 2-Jan-2018.)
Assertion
Ref Expression
nanbi2 ((φψ) → ((χ φ) ↔ (χ ψ)))

Proof of Theorem nanbi2
StepHypRef Expression
1 nanbi1 1295 . 2 ((φψ) → ((φ χ) ↔ (ψ χ)))
2 nancom 1290 . 2 ((χ φ) ↔ (φ χ))
3 nancom 1290 . 2 ((χ ψ) ↔ (ψ χ))
41, 2, 33bitr4g 279 1 ((φψ) → ((χ φ) ↔ (χ ψ)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176   wnan 1287
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  df-nan 1288
This theorem is referenced by:  nanbi12  1297  nanbi2i  1299  nanbi2d  1302
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