Theorem anbi1ci 626

Description: Variant of anbi1i 624 with commutation. (Contributed by Peter Mazsa, 7-Mar-2020.)

Hypothesis

Ref	Expression
anbi.1	⊢ (𝜑 ↔ 𝜓)

Assertion

Ref	Expression
anbi1ci	⊢ ((𝜒 ∧ 𝜑) ↔ (𝜓 ∧ 𝜒))

Proof of Theorem anbi1ci

Step	Hyp	Ref	Expression
1		anbi.1	. . 3 ⊢ (𝜑 ↔ 𝜓)
2	1	anbi2i 623	. 2 ⊢ ((𝜒 ∧ 𝜑) ↔ (𝜒 ∧ 𝜓))
3	2	biancomi 463	1 ⊢ ((𝜒 ∧ 𝜑) ↔ (𝜓 ∧ 𝜒))

Syntax hints:   ↔ wb 205   ∧ wa 396

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 206  df-an 397

This theorem is referenced by:  dfid3  5532  imai  6024  frpoind  6294  wfiOLD  6303  dfac5lem3  10057  cf0  10183  eqscut2  27129  coep  34195  brtxp  34432  sscoid  34465  brapply  34490  dfrdg4  34503  wl-df4-3mintru2  35925  rnxrncnvepres  36829  rnxrnidres  36830  pmapglb  38200  polval2N  38336  rp-fakeoranass  41728  alephiso2  41772