Theorem colleq2 45385

Description: Equality theorem for the collection operation. (Contributed by Rohan Ridenour, 11-Aug-2023.)

Assertion

Ref	Expression
colleq2	⊢ (𝐴 = 𝐵 → (𝐹 Coll 𝐴) = (𝐹 Coll 𝐵))

Proof of Theorem colleq2

Step	Hyp	Ref	Expression
1		eqidd 2764	. 2 ⊢ (𝐴 = 𝐵 → 𝐹 = 𝐹)
2		id 23	. 2 ⊢ (𝐴 = 𝐵 → 𝐴 = 𝐵)
3	1, 2	colleq12d 45383	1 ⊢ (𝐴 = 𝐵 → (𝐹 Coll 𝐴) = (𝐹 Coll 𝐵))

This proof depends on syntax axioms:   → wi 4   = wceq 1569   Coll ccoll 45380

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1944  ax-6 2001  ax-7 2042  ax-8 2148  ax-9 2156  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-3an 1105  df-tru 1572  df-fal 1582  df-ex 1812  df-sb 2101  df-clab 2742  df-cleq 2755  df-clel 2839  df-ral 3081  df-rex 3091  df-rab 3417  df-v 3456  df-ss 3901  df-dif 4050  df-in 4094  df-un 4154  df-nul 4282  df-if 4486  df-sn 4589  df-pr 4591  df-op 4839  df-iun 4956  df-br 5107  df-opab 5171  df-cnv 5663  df-dm 5665  df-rn 5666  df-res 5667  df-ima 5668  df-scott 9942  df-coll 45381

This theorem is used by: (None)