Theorem equcomi1 35054

Description: Proof of equcomi 2064 from equid1 35053, avoiding use of ax-5 1953 (the only use of ax-5 1953 is via ax7 2063, so using ax-7 2055 instead would remove dependency on ax-5 1953). (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 35053	. 2 ⊢ 𝑥 = 𝑥
2		ax7 2063	. 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 1839  ax-4 1853  ax-5 1953  ax-6 2021  ax-7 2055  ax-c5 35037  ax-c4 35038  ax-c7 35039  ax-c10 35040  ax-c9 35044

This theorem depends on definitions:  df-bi 199  df-an 387  df-ex 1824

This theorem is referenced by:  aecom-o  35055