Theorem ditgeq3i 36150

Description: Equality inference for the directed integral. (Contributed by GG, 1-Sep-2025.)

Hypothesis

Ref	Expression
ditgeq3i.1	⊢ 𝐶 = 𝐷

Assertion

Ref	Expression
ditgeq3i	⊢ ⨜[𝐴 → 𝐵]𝐶 d𝑥 = ⨜[𝐴 → 𝐵]𝐷 d𝑥

Proof of Theorem ditgeq3i

Step	Hyp	Ref	Expression
1		eqid 2734	. 2 ⊢ 𝐴 = 𝐴
2		eqid 2734	. 2 ⊢ 𝐵 = 𝐵
3		ditgeq3i.1	. 2 ⊢ 𝐶 = 𝐷
4	1, 2, 3	ditgeq123i 36148	1 ⊢ ⨜[𝐴 → 𝐵]𝐶 d𝑥 = ⨜[𝐴 → 𝐵]𝐷 d𝑥

Syntax hints:   = wceq 1539  ⨜cdit 25784

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2706

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1542  df-fal 1552  df-ex 1779  df-sb 2064  df-clab 2713  df-cleq 2726  df-clel 2808  df-ral 3051  df-rex 3060  df-rab 3414  df-v 3459  df-sbc 3764  df-csb 3873  df-dif 3927  df-un 3929  df-in 3931  df-ss 3941  df-nul 4307  df-if 4499  df-sn 4600  df-pr 4602  df-op 4606  df-uni 4881  df-br 5117  df-opab 5179  df-mpt 5199  df-xp 5657  df-cnv 5659  df-co 5660  df-dm 5661  df-rn 5662  df-res 5663  df-ima 5664  df-pred 6287  df-iota 6480  df-fv 6535  df-ov 7402  df-oprab 7403  df-mpo 7404  df-frecs 8274  df-wrecs 8305  df-recs 8379  df-rdg 8418  df-neg 11461  df-seq 14009  df-sum 15690  df-itg 25561  df-ditg 25785

This theorem is referenced by: (None)