Theorem axfrege58b 38194

Description: If ∀𝑥𝜑 is affirmed, [𝑦 / 𝑥]𝜑 cannot be denied. Identical to stdpc4 2353. Justification for ax-frege58b 38195. (Contributed by RP, 28-Mar-2020.)

Assertion

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

Proof of Theorem axfrege58b

Step	Hyp	Ref	Expression
1		stdpc4 2353	1 ⊢ (∀𝑥𝜑 → [𝑦 / 𝑥]𝜑)

Syntax hints:   → wi 4  ∀wal 1481  [wsb 1880

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-12 2047  ax-13 2246

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705  df-sb 1881

This theorem is referenced by: (None)