Theorem dfblockliftmap 39137

Description: Alternate definition of the block lift map. (Contributed by Peter Mazsa, 29-Jan-2026.) (Revised by Peter Mazsa, 22-Feb-2026.)

Assertion

Ref	Expression
dfblockliftmap	⊢ (𝑅 BlockLiftMap 𝐴) = (𝑚 ∈ dom (𝑅 ⋉ (◡ E ↾ 𝐴)) ↦ [𝑚](𝑅 ⋉ (◡ E ↾ 𝐴)))

Distinct variable groups:   𝐴,𝑚   𝑅,𝑚

Proof of Theorem dfblockliftmap

Step	Hyp	Ref	Expression
1		df-blockliftmap 39136	. 2 ⊢ (𝑅 BlockLiftMap 𝐴) = QMap (𝑅 ⋉ (◡ E ↾ 𝐴))
2		df-qmap 39123	. 2 ⊢ QMap (𝑅 ⋉ (◡ E ↾ 𝐴)) = (𝑚 ∈ dom (𝑅 ⋉ (◡ E ↾ 𝐴)) ↦ [𝑚](𝑅 ⋉ (◡ E ↾ 𝐴)))
3	1, 2	eqtri 2785	1 ⊢ (𝑅 BlockLiftMap 𝐴) = (𝑚 ∈ dom (𝑅 ⋉ (◡ E ↾ 𝐴)) ↦ [𝑚](𝑅 ⋉ (◡ E ↾ 𝐴)))

This proof depends on syntax axioms:   = wceq 1569   ↦ cmpt 5191   E cep 5559  ^◡ccnv 5659  dom cdm 5660   ↾ cres 5662  [cec 8690   ⋉ cxrn 38851   QMap cqmap 38852   BlockLiftMap cblockliftmap 38854

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1824  ax-4 1838  ax-5 1939  ax-6 1996  ax-7 2037  ax-9 2152  ax-ext 2734

This proof depends on definitions:  df-bi 210  df-an 401  df-ex 1809  df-cleq 2754  df-qmap 39123  df-blockliftmap 39136

This theorem is used by:  dfblockliftmap2  39138