Theorem axfrege58b 39150

Description: If ∀𝑥𝜑 is affirmed, [𝑦 / 𝑥]𝜑 cannot be denied. Identical to stdpc4 2428. Justification for ax-frege58b 39151. (Contributed by RP, 28-Mar-2020.)

Assertion

Ref	Expression
axfrege58b	⊢ (∀𝑥𝜑 → [𝑦 / 𝑥]𝜑)

Proof of Theorem axfrege58b

Step	Hyp	Ref	Expression
1		stdpc4 2428	1 ⊢ (∀𝑥𝜑 → [𝑦 / 𝑥]𝜑)

Syntax hints:   → wi 4  ∀wal 1599  [wsb 2011

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1839  ax-4 1853  ax-5 1953  ax-6 2021  ax-7 2055  ax-12 2163  ax-13 2334

This theorem depends on definitions:  df-bi 199  df-an 387  df-ex 1824  df-sb 2012

This theorem is referenced by: (None)