Theorem equcomi1 39009

Description: Proof of equcomi 2018 from equid1 39008, avoiding use of ax-5 1911 (the only use of ax-5 1911 is via ax7 2017, so using ax-7 2009 instead would remove dependency on ax-5 1911). (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 39008	. 2 ⊢ 𝑥 = 𝑥
2		ax7 2017	. 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 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-c5 38992  ax-c4 38993  ax-c7 38994  ax-c10 38995  ax-c9 38999

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1781

This theorem is referenced by:  aecom-o  39010