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Theorem orbi1i 506
 Description: Inference adding a right disjunct to both sides of a logical equivalence. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
orbi2i.1 (φψ)
Assertion
Ref Expression
orbi1i ((φ χ) ↔ (ψ χ))

Proof of Theorem orbi1i
StepHypRef Expression
1 orcom 376 . 2 ((φ χ) ↔ (χ φ))
2 orbi2i.1 . . 3 (φψ)
32orbi2i 505 . 2 ((χ φ) ↔ (χ ψ))
4 orcom 376 . 2 ((χ ψ) ↔ (ψ χ))
51, 3, 43bitri 262 1 ((φ χ) ↔ (ψ χ))
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 176   ∨ wo 357 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-or 359 This theorem is referenced by:  orbi12i  507  orordi  516  3anor  948  3or6  1263  19.45  1878  unass  3420  dfimak2  4298  ssfin  4470  eqtfinrelk  4486  evenoddnnnul  4514  nmembers1lem3  6270  nncdiv3  6277  nchoicelem6  6294  nchoicelem9  6297  nchoicelem18  6306
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