Theorem equcomi1 38923

Description: Proof of equcomi 2017 from equid1 38922, avoiding use of ax-5 1910 (the only use of ax-5 1910 is via ax7 2016, so using ax-7 2008 instead would remove dependency on ax-5 1910). (Contributed by BJ, 8-Jul-2021.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
equcomi1	⊢ (𝑥 = 𝑦 → 𝑦 = 𝑥)

Proof of Theorem equcomi1

Step	Hyp	Ref	Expression
1		equid1 38922	. 2 ⊢ 𝑥 = 𝑥
2		ax7 2016	. 2 ⊢ (𝑥 = 𝑦 → (𝑥 = 𝑥 → 𝑦 = 𝑥))
3	1, 2	mpi 20	1 ⊢ (𝑥 = 𝑦 → 𝑦 = 𝑥)

Syntax hints:   → wi 4

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-c5 38906  ax-c4 38907  ax-c7 38908  ax-c10 38909  ax-c9 38913

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1780

This theorem is referenced by:  aecom-o  38924