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	⊢ (φ ↔ ψ)

Assertion

Ref	Expression
orbi1i	⊢ ((φ ∨ χ) ↔ (ψ ∨ χ))

Proof of Theorem orbi1i

Step	Hyp	Ref	Expression
1		orcom 376	. 2 ⊢ ((φ ∨ χ) ↔ (χ ∨ φ))
2		orbi2i.1	. . 3 ⊢ (φ ↔ ψ)
3	2	orbi2i 505	. 2 ⊢ ((χ ∨ φ) ↔ (χ ∨ ψ))
4		orcom 376	. 2 ⊢ ((χ ∨ ψ) ↔ (ψ ∨ χ))
5	1, 3, 4	3bitri 262	1 ⊢ ((φ ∨ χ) ↔ (ψ ∨ χ))

Syntax hints:   ↔ wb 176   ∨ wo 357

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-or 359

This theorem is referenced by:  orbi12i  507  orordi  516  3anor  948  3or6  1263  19.45  1878  unass  3421  dfimak2  4299  ssfin  4471  eqtfinrelk  4487  evenoddnnnul  4515  nmembers1lem3  6271  nncdiv3  6278  nchoicelem6  6295  nchoicelem9  6298  nchoicelem18  6307