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Theorem ax7w 1718
 Description: Weak version of ax-7 1734 from which we can prove any ax-7 1734 instance not involving wff variables or bundling. Uses only Tarski's FOL axiom schemes. Unlike ax-7 1734, this theorem requires that x and y be distinct i.e. are not bundled. (Contributed by NM, 10-Apr-2017.)
Hypothesis
Ref Expression
ax7w.1 (y = z → (φψ))
Assertion
Ref Expression
ax7w (xyφyxφ)
Distinct variable groups:   y,z   x,y   φ,z   ψ,y
Allowed substitution hints:   φ(x,y)   ψ(x,z)

Proof of Theorem ax7w
StepHypRef Expression
1 ax7w.1 . 2 (y = z → (φψ))
21alcomiw 1704 1 (xyφyxφ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176  ∀wal 1540 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542 This theorem is referenced by: (None)
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