Theorem equcomi1 34185

Description: Proof of equcomi 1944 from equid1 34184, avoiding use of ax-5 1839 (the only use of ax-5 1839 is via ax7 1943, so using ax-7 1935 instead would remove dependency on ax-5 1839). (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 34184	. 2 ⊢ 𝑥 = 𝑥
2		ax7 1943	. 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 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-c5 34168  ax-c4 34169  ax-c7 34170  ax-c10 34171  ax-c9 34175

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705

This theorem is referenced by:  aecom-o  34186