Theorem aevlemALTOLD 2320

Description: Older alternate version of aevlem 1981. Obsolete as of 30-Mar-2021. (Contributed by NM, 22-Jul-2015.) (Proof shortened by Wolf Lammen, 17-Feb-2018.) (New usage is discouraged.) (Proof modification is discouraged.)

Assertion

Ref	Expression
aevlemALTOLD	⊢ (∀𝑧 𝑧 = 𝑤 → ∀𝑦 𝑦 = 𝑥)

Distinct variable group:   𝑧,𝑤

Proof of Theorem aevlemALTOLD

Dummy variable 𝑣 is distinct from all other variables.

Step	Hyp	Ref	Expression
1		cbvaev 1979	. 2 ⊢ (∀𝑧 𝑧 = 𝑤 → ∀𝑣 𝑣 = 𝑤)
2		axc11nlemALT 2306	. 2 ⊢ (∀𝑣 𝑣 = 𝑤 → ∀𝑧 𝑧 = 𝑣)
3		cbvaev 1979	. 2 ⊢ (∀𝑧 𝑧 = 𝑣 → ∀𝑥 𝑥 = 𝑣)
4		axc11nlemALT 2306	. 2 ⊢ (∀𝑥 𝑥 = 𝑣 → ∀𝑦 𝑦 = 𝑥)
5	1, 2, 3, 4	4syl 19	1 ⊢ (∀𝑧 𝑧 = 𝑤 → ∀𝑦 𝑦 = 𝑥)

Syntax hints:   → wi 4  ∀wal 1481

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-10 2019  ax-12 2047  ax-13 2246

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ex 1705  df-nf 1710

This theorem is referenced by: (None)