Theorem equcomi1 40100

Description: Proof of equcomi 2051 from equid1 40099, avoiding use of ax-5 1944 (the only use of ax-5 1944 is via ax7 2050, so using ax-7 2042 instead would remove dependency on ax-5 1944). (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 40099	. 2 ⊢ 𝑥 = 𝑥
2		ax7 2050	. 2 ⊢ (𝑥 = 𝑦 → (𝑥 = 𝑥 → 𝑦 = 𝑥))
3	1, 2	mpi 21	1 ⊢ (𝑥 = 𝑦 → 𝑦 = 𝑥)

This proof depends on syntax axioms:   → wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1944  ax-6 2001  ax-7 2042  ax-c5 40083  ax-c4 40084  ax-c7 40085  ax-c10 40086  ax-c9 40090

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1812

This theorem is used by:  aecom-o  40101