Theorem aevlemALTOLD 2308

Description: Older alternate version of aevlem 1968. 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 1966	. 2 ⊢ (∀𝑧 𝑧 = 𝑤 → ∀𝑣 𝑣 = 𝑤)
2		axc11nlemALT 2294	. 2 ⊢ (∀𝑣 𝑣 = 𝑤 → ∀𝑧 𝑧 = 𝑣)
3		cbvaev 1966	. 2 ⊢ (∀𝑧 𝑧 = 𝑣 → ∀𝑥 𝑥 = 𝑣)
4		axc11nlemALT 2294	. 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 1473

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-10 2006  ax-12 2034  ax-13 2234

This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701

This theorem is referenced by: (None)