Theorem calemesOLD 2777

Description: Obsolete proof of calemes 2776 as of 27-Sep-2022. (Contributed by David A. Wheeler, 27-Aug-2016.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
calemes.maj	⊢ ∀𝑥(𝜑 → 𝜓)
calemes.min	⊢ ∀𝑥(𝜓 → ¬ 𝜒)

Assertion

Ref	Expression
calemesOLD	⊢ ∀𝑥(𝜒 → ¬ 𝜑)

Proof of Theorem calemesOLD

Step	Hyp	Ref	Expression
1		calemes.min	. . . . 5 ⊢ ∀𝑥(𝜓 → ¬ 𝜒)
2	1	spi 2225	. . . 4 ⊢ (𝜓 → ¬ 𝜒)
3	2	con2i 137	. . 3 ⊢ (𝜒 → ¬ 𝜓)
4		calemes.maj	. . . 4 ⊢ ∀𝑥(𝜑 → 𝜓)
5	4	spi 2225	. . 3 ⊢ (𝜑 → 𝜓)
6	3, 5	nsyl 138	. 2 ⊢ (𝜒 → ¬ 𝜑)
7	6	ax-gen 1894	1 ⊢ ∀𝑥(𝜒 → ¬ 𝜑)

Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1654

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1894  ax-4 1908  ax-5 2009  ax-6 2075  ax-7 2112  ax-12 2220

This theorem depends on definitions:  df-bi 199  df-ex 1879

This theorem is referenced by: (None)