Theorem wl-hbae1 37502

Description: This specialization of hbae 2430 does not depend on ax-11 2158. (Contributed by Wolf Lammen, 8-Aug-2021.)

Assertion

Ref	Expression
wl-hbae1	⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑦∀𝑥 𝑥 = 𝑦)

Proof of Theorem wl-hbae1

Step	Hyp	Ref	Expression
1		axc11n 2425	. 2 ⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑦 𝑦 = 𝑥)
2		axc11n 2425	. . 3 ⊢ (∀𝑦 𝑦 = 𝑥 → ∀𝑥 𝑥 = 𝑦)
3	2	axc4i 2321	. 2 ⊢ (∀𝑦 𝑦 = 𝑥 → ∀𝑦∀𝑥 𝑥 = 𝑦)
4	1, 3	syl 17	1 ⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑦∀𝑥 𝑥 = 𝑦)

Syntax hints:   → wi 4  ∀wal 1538

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-10 2142  ax-12 2178  ax-13 2371

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-ex 1780  df-nf 1784

This theorem is referenced by: (None)