Theorem dfblockliftmap 39312

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 39311	. 2 ⊢ (𝑅 BlockLiftMap 𝐴) = QMap (𝑅 ⋉ (◡ E ↾ 𝐴))
2		df-qmap 39298	. 2 ⊢ QMap (𝑅 ⋉ (◡ E ↾ 𝐴)) = (𝑚 ∈ dom (𝑅 ⋉ (◡ E ↾ 𝐴)) ↦ [𝑚](𝑅 ⋉ (◡ E ↾ 𝐴)))
3	1, 2	eqtri 2783	1 ⊢ (𝑅 BlockLiftMap 𝐴) = (𝑚 ∈ dom (𝑅 ⋉ (◡ E ↾ 𝐴)) ↦ [𝑚](𝑅 ⋉ (◡ E ↾ 𝐴)))

This proof depends on syntax axioms:   = wceq 1570   ↦ cmpt 5185   E cep 5546  ^◡ccnv 5646  dom cdm 5647   ↾ cres 5649  [cec 8693   ⋉ cxrn 39026   QMap cqmap 39027   BlockLiftMap cblockliftmap 39029

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-9 2155  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1813  df-cleq 2752  df-qmap 39298  df-blockliftmap 39311

This theorem is used by:  dfblockliftmap2  39313