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Theorem aevlemALTOLD 2319
Description: Older alternate version of aevlem 1978. 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.
StepHypRef Expression
1 cbvaev 1976 . 2 (∀𝑧 𝑧 = 𝑤 → ∀𝑣 𝑣 = 𝑤)
2 axc11nlemALT 2305 . 2 (∀𝑣 𝑣 = 𝑤 → ∀𝑧 𝑧 = 𝑣)
3 cbvaev 1976 . 2 (∀𝑧 𝑧 = 𝑣 → ∀𝑥 𝑥 = 𝑣)
4 axc11nlemALT 2305 . 2 (∀𝑥 𝑥 = 𝑣 → ∀𝑦 𝑦 = 𝑥)
51, 2, 3, 44syl 19 1 (∀𝑧 𝑧 = 𝑤 → ∀𝑦 𝑦 = 𝑥)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1478
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-10 2016  ax-12 2044  ax-13 2245
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ex 1702  df-nf 1707
This theorem is referenced by: (None)
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