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  5492  imai  5982  frpoind  6245  wfiOLD  6254  dfac5lem3  9881  cf0  10007  coep  33719  eqscut2  34000  brtxp  34182  sscoid  34215  brapply  34240  dfrdg4  34253  wl-df4-3mintru2  35658  rnxrncnvepres  36526  rnxrnidres  36527  pmapglb  37784  polval2N  37920  rp-fakeoranass  41121  alephiso2  41165