Theorem anbi1ci 635

Description: Variant of anbi1i 633 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 632	. 2 ⊢ ((𝜒 ∧ 𝜑) ↔ (𝜒 ∧ 𝜓))
3	2	biancomi 466	1 ⊢ ((𝜒 ∧ 𝜑) ↔ (𝜓 ∧ 𝜒))

Syntax hints:   ↔ wb 208   ∧ wa 399

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 209  df-an 400

This theorem is referenced by:  dfid3  5541  imai  6059  frpoind  6324  dfac5lem3  10075  cf0  10201  eqcuts2  27867  coep  36063  brtxp  36189  sscoid  36222  brapply  36247  dfrdg4  36262  wl-df4-3mintru2  37942  rnxrncnvepres  38883  rnxrnidres  38884  pmapglb  40355  polval2N  40491  rp-fakeoranass  44051  alephiso2  44095