Theorem symdifeq2 4240

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 4239	. 2 ⊢ (𝐴 = 𝐵 → (𝐴 △ 𝐶) = (𝐵 △ 𝐶))
2		symdifcom 4238	. 2 ⊢ (𝐶 △ 𝐴) = (𝐴 △ 𝐶)
3		symdifcom 4238	. 2 ⊢ (𝐶 △ 𝐵) = (𝐵 △ 𝐶)
4	1, 2, 3	3eqtr4g 2791	1 ⊢ (𝐴 = 𝐵 → (𝐶 △ 𝐴) = (𝐶 △ 𝐵))

Syntax hints:   → wi 4   = wceq 1533   △ csymdif 4236

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2697

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2704  df-cleq 2718  df-clel 2804  df-rab 3427  df-v 3470  df-dif 3946  df-un 3948  df-symdif 4237

This theorem is referenced by: (None)