Theorem equcomi1 39525

Description: Proof of equcomi 2038 from equid1 39524, avoiding use of ax-5 1931 (the only use of ax-5 1931 is via ax7 2037, so using ax-7 2029 instead would remove dependency on ax-5 1931). (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 39524	. 2 ⊢ 𝑥 = 𝑥
2		ax7 2037	. 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 1816  ax-4 1830  ax-5 1931  ax-6 1988  ax-7 2029  ax-c5 39508  ax-c4 39509  ax-c7 39510  ax-c10 39511  ax-c9 39515

This theorem depends on definitions:  df-bi 209  df-an 400  df-ex 1801

This theorem is referenced by:  aecom-o  39526