Theorem bj-dtrucor 33326

Description: Remove dependency on ax-13 2391 from dtrucor 5072. (Contributed by BJ, 16-Jul-2019.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
bj-dtrucor.1	⊢ 𝑥 = 𝑦

Assertion

Ref	Expression
bj-dtrucor	⊢ 𝑥 ≠ 𝑦

Distinct variable group:   𝑥,𝑦

Proof of Theorem bj-dtrucor

Step	Hyp	Ref	Expression
1		bj-dtru 33323	. . 3 ⊢ ¬ ∀𝑥 𝑥 = 𝑦
2	1	pm2.21i 117	. 2 ⊢ (∀𝑥 𝑥 = 𝑦 → 𝑥 ≠ 𝑦)
3		bj-dtrucor.1	. 2 ⊢ 𝑥 = 𝑦
4	2, 3	mpg 1898	1 ⊢ 𝑥 ≠ 𝑦

Syntax hints:  ∀wal 1656   ≠ wne 3000

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1896  ax-4 1910  ax-5 2011  ax-6 2077  ax-7 2114  ax-8 2168  ax-9 2175  ax-10 2194  ax-11 2209  ax-12 2222  ax-nul 5014  ax-pow 5066

This theorem depends on definitions:  df-bi 199  df-an 387  df-tru 1662  df-ex 1881  df-nf 1885

This theorem is referenced by: (None)