Theorem ditgeq3i 36253

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 2731	. 2 ⊢ 𝐴 = 𝐴
2		eqid 2731	. 2 ⊢ 𝐵 = 𝐵
3		ditgeq3i.1	. 2 ⊢ 𝐶 = 𝐷
4	1, 2, 3	ditgeq123i 36251	1 ⊢ ⨜[𝐴 → 𝐵]𝐶 d𝑥 = ⨜[𝐴 → 𝐵]𝐷 d𝑥

Syntax hints:   = wceq 1541  ⨜cdit 25774

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2113  ax-9 2121  ax-ext 2703

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1544  df-fal 1554  df-ex 1781  df-sb 2068  df-clab 2710  df-cleq 2723  df-clel 2806  df-ral 3048  df-rex 3057  df-rab 3396  df-v 3438  df-sbc 3737  df-csb 3846  df-dif 3900  df-un 3902  df-in 3904  df-ss 3914  df-nul 4281  df-if 4473  df-sn 4574  df-pr 4576  df-op 4580  df-uni 4857  df-br 5090  df-opab 5152  df-mpt 5171  df-xp 5620  df-cnv 5622  df-co 5623  df-dm 5624  df-rn 5625  df-res 5626  df-ima 5627  df-pred 6248  df-iota 6437  df-fv 6489  df-ov 7349  df-oprab 7350  df-mpo 7351  df-frecs 8211  df-wrecs 8242  df-recs 8291  df-rdg 8329  df-neg 11347  df-seq 13909  df-sum 15594  df-itg 25551  df-ditg 25775

This theorem is referenced by: (None)