Theorem symdifeq2 4176

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 4175	. 2 ⊢ (𝐴 = 𝐵 → (𝐴 △ 𝐶) = (𝐵 △ 𝐶))
2		symdifcom 4174	. 2 ⊢ (𝐶 △ 𝐴) = (𝐴 △ 𝐶)
3		symdifcom 4174	. 2 ⊢ (𝐶 △ 𝐵) = (𝐵 △ 𝐶)
4	1, 2, 3	3eqtr4g 2804	1 ⊢ (𝐴 = 𝐵 → (𝐶 △ 𝐴) = (𝐶 △ 𝐵))

Syntax hints:   → wi 4   = wceq 1539   △ csymdif 4172

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2110  ax-9 2118  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 844  df-tru 1542  df-ex 1784  df-sb 2069  df-clab 2716  df-cleq 2730  df-clel 2817  df-rab 3072  df-v 3424  df-dif 3886  df-un 3888  df-symdif 4173

This theorem is referenced by: (None)