Theorem wl-hbae1 34751

Description: This specialization of hbae 2447 does not depend on ax-11 2154. (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 2442	. 2 ⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑦 𝑦 = 𝑥)
2		axc11n 2442	. . 3 ⊢ (∀𝑦 𝑦 = 𝑥 → ∀𝑥 𝑥 = 𝑦)
3	2	axc4i 2335	. 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 1529

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1905  ax-6 1964  ax-7 2009  ax-10 2139  ax-12 2170  ax-13 2384

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-ex 1775  df-nf 1779

This theorem is referenced by: (None)