Theorem equcomi1 33203

Description: Proof of equcomi 1931 from equid1 33202, avoiding use of ax-5 1827 (the only use of ax-5 1827 is via ax7 1930, so using ax-7 1922 instead would remove dependency on ax-5 1827). (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 33202	. 2 ⊢ 𝑥 = 𝑥
2		ax7 1930	. 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 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-c5 33186  ax-c4 33187  ax-c7 33188  ax-c10 33189  ax-c9 33193

This theorem depends on definitions:  df-bi 196  df-an 385  df-ex 1696

This theorem is referenced by:  aecom-o  33204