Theorem a4b 927

Description: A weaker version of a4a 842.

Hypothesis

Ref	Expression
a4b.1	⊢ (x = y → (φ → ψ))

Assertion

Ref	Expression
a4b	⊢ (∀xφ → ψ)

Distinct variable group(s):   ψ,x

Proof of Theorem a4b

Step	Hyp	Ref	Expression
1		ax-17 925	. 2 ⊢ (ψ → ∀xψ)
2		a4b.1	. 2 ⊢ (x = y → (φ → ψ))
3	1, 2	a4a 842	1 ⊢ (∀xφ → ψ)

Syntax hints:   → wi 2  ∀wal 672   = weq 797

This theorem is referenced by:  a4b1 928

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-gen 677  ax-9 799  ax-17 925

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679

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