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Metamath Proof Explorer

Theorem ax11w

Description: Weak version of ax-11 from which we can prove any ax-11 instance not involving wff variables or bundling. Uses only Tarski's FOL axiom schemes. Unlike ax-11 , this theorem requires that x and y be distinct i.e. are not bundled. It is an alias of alcomimw introduced for labeling consistency. (Contributed by NM, 10-Apr-2017) Use alcomimw instead. (New usage is discouraged.)

		Ref	Expression
	Hypothesis	ax11w.1	⊢ ( 𝑦 = 𝑧 → ( 𝜑 ↔ 𝜓 ) )
	Assertion	ax11w	⊢ ( ∀ 𝑥 ∀ 𝑦 𝜑 → ∀ 𝑦 ∀ 𝑥 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		ax11w.1	⊢ ( 𝑦 = 𝑧 → ( 𝜑 ↔ 𝜓 ) )
2	1	alcomimw	⊢ ( ∀ 𝑥 ∀ 𝑦 𝜑 → ∀ 𝑦 ∀ 𝑥 𝜑 )