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Metamath Proof Explorer
Description: Variant of anbi1i with commutation. (Contributed by Peter Mazsa, 7-Mar-2020)
|
|
Ref |
Expression |
|
Hypothesis |
anbi.1 |
⊢ ( 𝜑 ↔ 𝜓 ) |
|
Assertion |
anbi1ci |
⊢ ( ( 𝜒 ∧ 𝜑 ) ↔ ( 𝜓 ∧ 𝜒 ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
anbi.1 |
⊢ ( 𝜑 ↔ 𝜓 ) |
| 2 |
1
|
anbi2i |
⊢ ( ( 𝜒 ∧ 𝜑 ) ↔ ( 𝜒 ∧ 𝜓 ) ) |
| 3 |
2
|
biancomi |
⊢ ( ( 𝜒 ∧ 𝜑 ) ↔ ( 𝜓 ∧ 𝜒 ) ) |