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Metamath Proof Explorer
Description: Introduce a left anti-conjunct to both sides of a logical equivalence.
(Contributed by SF, 2-Jan-2018)
|
|
Ref |
Expression |
|
Hypothesis |
nanbid.1 |
⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) ) |
|
Assertion |
nanbi2d |
⊢ ( 𝜑 → ( ( 𝜃 ⊼ 𝜓 ) ↔ ( 𝜃 ⊼ 𝜒 ) ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
nanbid.1 |
⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) ) |
| 2 |
|
nanbi2 |
⊢ ( ( 𝜓 ↔ 𝜒 ) → ( ( 𝜃 ⊼ 𝜓 ) ↔ ( 𝜃 ⊼ 𝜒 ) ) ) |
| 3 |
1 2
|
syl |
⊢ ( 𝜑 → ( ( 𝜃 ⊼ 𝜓 ) ↔ ( 𝜃 ⊼ 𝜒 ) ) ) |