Theorem symdifeq2 4236

Description: Equality theorem for symmetric difference. (Contributed by Scott Fenton, 24-Apr-2012.)

Assertion

Ref	Expression
symdifeq2	⊢ (𝐴 = 𝐵 → (𝐶 △ 𝐴) = (𝐶 △ 𝐵))

Proof of Theorem symdifeq2

Step	Hyp	Ref	Expression
1		symdifeq1 4235	. 2 ⊢ (𝐴 = 𝐵 → (𝐴 △ 𝐶) = (𝐵 △ 𝐶))
2		symdifcom 4234	. 2 ⊢ (𝐶 △ 𝐴) = (𝐴 △ 𝐶)
3		symdifcom 4234	. 2 ⊢ (𝐶 △ 𝐵) = (𝐵 △ 𝐶)
4	1, 2, 3	3eqtr4g 2796	1 ⊢ (𝐴 = 𝐵 → (𝐶 △ 𝐴) = (𝐶 △ 𝐵))

Syntax hints:   → wi 4   = wceq 1540   △ csymdif 4232

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1543  df-ex 1780  df-sb 2066  df-clab 2715  df-cleq 2728  df-clel 2810  df-rab 3421  df-v 3466  df-dif 3934  df-un 3936  df-symdif 4233

This theorem is referenced by: (None)