Theorem equcomi1 39694

Description: Proof of equcomi 2047 from equid1 39693, avoiding use of ax-5 1940 (the only use of ax-5 1940 is via ax7 2046, so using ax-7 2038 instead would remove dependency on ax-5 1940). (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 39693	. 2 ⊢ 𝑥 = 𝑥
2		ax7 2046	. 2 ⊢ (𝑥 = 𝑦 → (𝑥 = 𝑥 → 𝑦 = 𝑥))
3	1, 2	mpi 21	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 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038  ax-c5 39677  ax-c4 39678  ax-c7 39679  ax-c10 39680  ax-c9 39684

This theorem depends on definitions:  df-bi 210  df-an 401  df-ex 1810

This theorem is referenced by:  aecom-o  39695